\letter {}
  (Near-)Additive Magma Categories, \indexit{557}
  (Near-)Additive Magma Generation, \indexit{558}
  `+', 48
  `-', 48
  `-A', 30
  `-B', 30
  `-C', 31
  `-D', 30
  `-K', 29
  `-L', 29
  `-M', 30
  `-N', 30
  `-O', 30
  `-P', 31
    \sub on Macintosh, 31
  `-R', 29
  `-T', 31
  `-U', 31
  `-W', 31
    \sub on Macintosh, 32
  `-X', 31
  `-Y', 31
  `-a', 30
    \sub on Macintosh, 32
  `-b', 27
  `-e', 27
    \sub on Macintosh, 32
  `-f', 27
    \sub on Macintosh, 32
  `-g', 28
  `-g -g', 28
  `-h', 27
  `-i', 31
  `-l', 29
  `-m', 28
  `-n', 28
    \sub on Macintosh, 32
  `-o', 28
    \sub on Macintosh, 32
  `-p', 31
  `-q', 27
  `-r', 29
  `-x', 28
  `-y', 28
  `-z', 31
    \sub on Macintosh, 31
  `.gaprc', 33
  `/', 48
    \sub for character tables, 733
  `\*', 48
    \sub for character tables, 733
  `\\\char 39', 251
  `\\XYZ', 251
  `\\\"', 251
  `\\\\', 251
  `\\b', 251
  `\\c', 251
  `\\in', operation for testing membership, 276
  `\\n', 251
  `\\r', 251
  `{\accent 94 }', 48
    \sub for class functions, 772
  1-Cohomology, \indexit{379}
  2-Cohomology and Extensions, \indexit{458}
\letter A
  `AbelianGroup', 511
  `AbelianInvariants', for character tables, 735
    \sub for groups, 368
  Abelian Invariants for Subgroups, \indexit{478}
  `AbelianInvariantsMultiplier', 382
  `AbelianInvariantsNormalClosureFpGroup', 478
  `Abelian\-Invariants\-Normal\-Closure\-Fp\-Group\-Rrs', 478
  `AbelianInvariantsOfList', 243
  `AbelianInvariantsSubgroupFpGroup', 478
  `AbelianInvariantsSubgroupFpGroupMtc', 478
  `AbelianInvariantsSubgroupFpGroupRrs', 478
  `AbelianNumberField', 591
  abelian number field, 593
  abelian number fields, canonicalbasis, 594
  abelian number fields, Galois group, 596
  `AbelianSubfactorAction', 404
  About Group Actions, \indexit{396}
  `AbsInt', 127
  `AbsoluteIrreducibleModules', 753
  `AbsoluteValue', 159
  absolute value of an integer, 127
  `AbsolutIrreducibleModules', 753
  abstract word, 325
  `AbstractWordTietzeWord', 487
  accessing, list elements, 174
    \sub record elements, 262
  Accessing a Module, \indexit{697}
  Accessing Record Elements, \indexit{262}
  Accessing Subgroups via Tables of Marks, \indexit{718}
  `AClosestVectorCombinationsMatFFEVecFFE', 219
  `AClosest\-Vector\-Combinations\-Mat\-FFEVec\-FFECoords', 219
  `ActingAlgebra', 634
  `ActingDomain', 408
  Acting OnRight and OnLeft, \indexit{434}
  `Action', 403
  action, by conjugation, 397
    \sub on blocks, 397
    \sub on sets, 397
  `ActionHomomorphism', 402
  Action of a group on itself, \indexit{404}
  Action on Subfactors Defined by a Pcgs, \indexit{449}
  actions, 397
  Actions of Matrix Groups, \indexit{430}
  `ActorOfExternalSet', 410
  `Add', 177
  add, an element to a set, 197
  `AddCoeffs', 217
  `AddGenerator', 489
  `AddGenerators', 345
  `AddGeneratorsExtendSchreierTree', 426
  addition, 48
    \sub list and non-list, 186
    \sub matrices, 223
    \sub matrix and scalar, 223
    \sub operation, 296
    \sub rational functions, 670
    \sub scalar and matrix, 223
    \sub scalar and matrix list, 225
    \sub scalar and vector, 215
    \sub vector and scalar, 215
    \sub vectors, 215
  Additive Arithmetic for Lists, \indexit{186}
  `AdditiveInverse', 294
  `AdditiveInverseAttr', 294
  `AdditiveInverseImmutable', 294
  `AdditiveInverseMutable', 294
  `AdditiveInverseOp', 294
  `AdditiveInverseSameMutability', 294
  `AdditiveInverseSM', 294
  `AdditiveNeutralElement', 559
  `AddRelator', 489
  `AddRowVector', 217
  `AddRule', 345
  `AddRuleReduced', 345
  `AddSet', 197
  `AdjointAssociativeAlgebra', 651
  `AdjointBasis', 623
  `AdjointMatrix', 651
  `AdjointModule', 636
  Advanced Features of GAP, \indexit{30}
  Advanced List Manipulations, \indexit{205}
  Advanced Methods for Dixon-Schneider Calculations, \indexit{754}
  `AffineAction', 449
  `AffineActionLayer', 449
  `AffineOperation', 449
  `AffineOperationLayer', 449
  `Agemo', 365
  `Algebra', 614
  `AlgebraByStructureConstants', 617
  `AlgebraGeneralMappingByImages', 628
  `AlgebraHomomorphismByImages', 628
  `AlgebraHomomorphismByImagesNC', 628
  `AlgebraicExtension', 691
  `AlgebraWithOne', 614
  `AlgebraWithOneGeneralMappingByImages', 629
  `AlgebraWithOneHomomorphismByImages', 629
  `AlgebraWithOneHomomorphismByImagesNC', 629
  `AllBlocks', 407
  `AllIrreducibleSolvableGroups', 529
  `All<Library>Groups', 517
  `AllPrimitiveGroups', 517
  `AllSmallGroups', 520
  `AllTransitiveGroups', 517
  `Alpha', 824
  `AlternatingGroup', 511
  `and', 170
    \sub for filters, 117, 171
  An Example of Advanced Dixon-Schneider Calculations, \indexit{755}
  `ANFAutomorphism', 596
  `AntiSymmetricParts', 789
  antisymmetric relation, 315
  `Append', 178
  `AppendTo', 95
    \sub for streams, 101
  Apple, 840, 841
  `ApplicableMethod', 78
  ApplicableMethod, \indexit{78}
  `ApplicableMethodTypes', 78
  `Apply', 200
  `ApplySimpleReflection', 648
  `ApproximateSuborbitsStabilizerPermGroup', 424
  `ARCH_IS_MAC', 35
  `ARCH_IS_UNIX', 35
  `ARCH_IS_WINDOWS', 35
  `arg', special function argument, 46, 56
  Arithmetic for External Representations of Polynomials, \indexit{690}
  Arithmetic for Lists, \indexit{184}
  Arithmetic Operations for Class Functions, \indexit{771}
  Arithmetic Operations for Elements, \indexit{296}
  Arithmetic Operations for General Mappings, \indexit{309}
  Arithmetic Operators, \indexit{48}
  `Arrangements', 149
  arrow notation for functions, 57
  `AsAlgebra', 623
  `AsAlgebraWithOne', 624
  `AsBinaryRelationOnPoints', 316
  `AsBlockMatrix', 239
  `AscendingChain', 371
  `AsDivisionRing', 578
  `AsDuplicateFreeList', 199
  `AsField', 578
  `AsFreeLeftModule', 575
  `AsGroup', 350
  `AsGroupGeneralMappingByImages', 386
  `AsLeftIdeal', 565
  `AsLeftModule', 573
  `AsList', 271
  `AsMagma', 320
  `AsMonoid', 545
  `AsPolynomial', 672
  `AsRightIdeal', 565
  `AsRing', 562
  `AsSemigroup', 538
  `Assert', 81
  `AssertionLevel', 81
  Assertions, \indexit{81}
  `AsSet', 271
  `AssignGeneratorVariables', 332
  assignment, to a list, 176
    \sub to a record, 262
    \sub variable, 50
  Assignments, \indexit{50}
  `AssignNiceMonomorphismAutomorphismGroup', 392
  `AssociatedPartition', 154
  `AssociatedReesMatrixSemigroupOfDClass', 544
  `Associates', 568
  associativity, 48
  `AssocWordByLetterRep', 337
  `AsSortedList', 271
  `AsSSortedList', 271
  `As<Struct>', 288
  `AsSubalgebra', 624
  `AsSubalgebraWithOne', 624
  `AsSubgroup', 351
  `AsSubgroupOfWholeGroupByQuotient', 476
  `AsSubmagma', 321
  `AsSubmonoid', 545
  `AsSubsemigroup', 538
  `AsSubspace', 599
  `AsSub<struct>', 291
  `AsTransformation', 555
  `AsTransformationNC', 555
  `AsTwoSidedIdeal', 565
  `AsVectorSpace', 598
  at exit functions, 73
  ATLAS Irrationalities, \indexit{161}
  `AtlasIrrationality', 163
  atomic irrationalities, 161
  Attributes, \indexit{121}
  Attributes and Operations for Algebras, \indexit{622}
  Attributes and Properties for (Near-)Additive Magmas, \indexit{559}
  Attributes and Properties for Collections, \indexit{272}
  Attributes and Properties for Magmas, \indexit{322}
  Attributes and Properties for Matrix Groups, \indexit{429}
  Attributes and Properties of Character Tables, \indexit{733}
  Attributes and Properties of Elements, \indexit{292}
  Attributes of and Operations on Equivalence Relations, \indexit{317}
  Attributes of Tables of Marks, \indexit{708}
  `AttributeValueNotSet', 122
  `AugmentationIdeal', 663
  `AugmentedCosetTableInWholeGroup', 470
  `AugmentedCosetTableMtc', 470
  `AugmentedCosetTableRrs', 470
  Augmented Coset Tables and Rewriting, \indexit{470}
  automatic loading of gap packages, 845
  `AutomorphismDomain', 391
  `AutomorphismGroup', 391
    \sub for groups with pcgs, 450
  automorphism group, of number fields, 596
  Automorphisms and Equivalence of Character Tables, \indexit{762}
  `AutomorphismsOfTable', 737
\letter B
  $b_N$, 161
  backslash character, 251
  backspace character, 251
  `Backtrace', GAP3 name for `Where', 70
  Backtrack, \indexit{426}
  `BANNER', 850
  `BaseFixedSpace', 230
  `BaseIntersectionIntMats', 240
  `BaseIntMat', 240
  `BaseMat', 233
  `BaseMatDestructive', 233
  `BaseOfGroup', 423
  `BaseOrthogonalSpaceMat', 233
  Bases of Vector Spaces, \indexit{600}
  `BaseStabChain', 423
  `BaseSteinitzVectors', 233
  Basic Actions, \indexit{397}
  Basic Groups, \indexit{510}
  Basic Operations for Class Functions, \indexit{769}
  Basic Operations for Lists, \indexit{174}
  `BasicWreathProductOrdering', 284
  `Basis', 601
  `BasisNC', 601
  `BasisVectors', 602
  `Bell', 148
  `Bernoulli', 148
  `BestQuoInt', 129
  `BestSplittingMatrix', 754
  `BiAlgebraModule', 632
  `BiAlgebraModuleByGenerators', 632
  `BilinearFormMat', 647
  binary relation, 314
  `BinaryRelationByElements', 314
  `BinaryRelationOnPoints', 316
  `BinaryRelationOnPointsNC', 316
  Binary Relations on Points, \indexit{316}
  `BinaryRelationTransformation', 556
  `BindGlobal', 45
  `Binomial', 147
  blank, 41
  `BlistList', 210
  Block Matrices, \indexit{239}
  `BlockMatrix', 239
  `Blocks', 407
  `BlocksInfo', 742
  Block Systems, \indexit{407}
  `BlownUpMat', 235
  `BlownUpVector', 235
  `BlowUpIsomorphism', 430
  BNF, 59
  body, 55
  `BombieriNorm', 678
  Boolean Lists Representing Subsets, \indexit{210}
  bound, 43
  Brauer character, 776
  `BrauerCharacterValue', 799
  `BrauerTable', 727
  `BrauerTableOp', 727
  `BravaisGroup', 433
  `BravaisSubgroups', 433
  `BravaisSupergroups', 433
  Break, \indexit{55}
  break loop message, 70
  Break Loops, \indexit{67}
  `break' statement, 55
  browsing backwards, 22
  browsing backwards one chapter, 23
  browsing forward, 22
  browsing forward one chapter, 23
  browsing the next section browsed, 23
  browsing the previous section browsed, 23
  Browsing through the Sections, \indexit{22}
  bug reports, see If Things Go Wrong, 837
  Building new orderings, \indexit{280}
\letter C
  $c_N$, 161
  Calculating with Group Automorphisms, \indexit{392}
  Calendar Arithmetic, \indexit{258}
  `CallFuncList', 62
  Calling a function with a list argument that is interpreted as several arguments, \indexit{62}
  Cancellation Tests for Rational Functions, \indexit{690}
  `CanComputeIndex', 383
  `CanComputeIsSubset', 383
  `CanComputeSize', 383
  `CanComputeSizeAnySubgroup', 383
  candidates, for permutation characters, 792, 795
  `CanEasilyCompareElements', 295
  `CanEasilyCompareElementsFamily', 295
  `CanEasilyComputePcgs', 436
  `CanEasilySortElements', 295
  `CanEasilySortElementsFamily', 295
  `CanEasilyTestMembership', 383
  `CanonicalBasis', 601
  canonical basis, for matrix spaces, 608
    \sub for row spaces, 608
  `CanonicalGenerators', 647
  `CanonicalPcElement', 438
  `CanonicalPcgs', 441
  `CanonicalPcgsByGeneratorsWithImages', 443
  `Canonical\-Representative\-Determinator\-Of\-External\-Set', 410
  `CanonicalRepresentativeOfExternalSet', 410
  `CanonicalRightCosetElement', 357
  Carmichael's lambda function, 139
  carriage return character, 251
  `CartanMatrix', 646
  `CartanSubalgebra', 643
  `Cartesian', 201
  Categories, \indexit{118}
  Categories and Properties of Algebras, \indexit{621}
  Categories for Streams and the StreamsFamily, \indexit{97}
  Categories of Associative Words, \indexit{330}
  Categories of Matrices, \indexit{222}
  `CategoriesOfObject', 120
  Categories of Words and Nonassociative Words, \indexit{325}
  `CategoryCollections', 268
  `Center', 323
  center, 322
  `CentralCharacter', 780
  central character, 780
  `CentralIdempotentsOfAlgebra', 626
  centraliser, 322
  `Centralizer', 322
    \sub for groups with pcgs, 450
  `CentralizerInGLnZ', 433
  `CentralizerModulo', 372
  `CentralizerSizeLimitConsiderFunction', 451
  `CentralNormalSeriesByPcgs', 445
  `Centre', 323
    \sub for groups with pcgs, 450
  centre, of a character, 779
  `CentreOfCharacter', 779
  `CF', 591
  `ChangeStabChain', 425
  Changing Presentations, \indexit{489}
  Changing the Help Viewer, \indexit{23}
  Changing the Representation, \indexit{289}
  Changing the Structure, \indexit{288}
  `CHAR_INT', 257
  `CHAR_SINT', 257
  `Character', 774
  Character Conversion, \indexit{257}
  `CharacterDegrees', 733
  Character Degrees and Derived Length, \indexit{824}
  `Characteristic', 292
  characteristic, for class functions, 773
  `CharacteristicPolynomial', 234
  characteristic polynomial, for field elements, 580
  `CharacterNames', 737
  `CharacterParameters', 738
  characters, 767
    \sub permutation, 792, 795
    \sub symmetrizations of, 788
  `CharacterTable', 727
  Character Table Categories, \indexit{729}
  `CharacterTableDirectProduct', 757
  `CharacterTableFactorGroup', 758
  `CharacterTableIsoclinic', 759
  `CharacterTableRegular', 728
  character tables, 726
    \sub access to, 726
    \sub calculate, 726
    \sub infix operators, 733
    \sub of groups, 726
  `CharacterTableWithSortedCharacters', 760
  `CharacterTableWithSortedClasses', 760
  `CharacterTableWreathSymmetric', 759
  character value, of group element using powering operator, 772
  `CharsFamily', 253
  `CheapFactorsInt', 134
  `CheckFixedPoints', 813
  `CheckForHandlingByNiceBasis', 613
  `CheckPermChar', 820
  `ChevalleyBasis', 645
  `ChiefNormalSeriesByPcgs', 446
  `ChiefSeries', 369
  `ChiefSeriesThrough', 369
  `ChiefSeriesUnderAction', 369
  `ChineseRem', 130
  Chinese remainder, 131
  `Chomp', 256
  `CIUnivPols', 670
  `ClassElementLattice', 374
  classes, real, 739
  `ClassesSolvableGroup', 450
  `ClassFunction', 774
  class function, 767
  class function objects, 767
  class functions, 810
    \sub as ring elements, 771
  `ClassFunctionSameType', 775
  Class Fusions between Character Tables, \indexit{805}
  Classical Groups, \indexit{512}
  `ClassMultiplicationCoefficient', for character tables, 746
  class multiplication coefficient, 746, 747
  `ClassNames', 737
  `ClassNamesTom', 709
  `ClassOrbit', 739
  `ClassParameters', 738
  `ClassPermutation', 761
  `ClassPositionsOfAgemo', 739
  `ClassPositionsOfCentre', for characters, 779
    \sub for character tables, 739
  `ClassPositionsOfDerivedSubgroup', 740
  `Class\-Positions\-Of\-Direct\-Product\-Decompositions', 740
  `ClassPositionsOfElementaryAbelianSeries', 740
  `ClassPositionsOfFittingSubgroup', 740
  `ClassPositionsOfKernel', 778
  `ClassPositionsOfLowerCentralSeries', 740
  `ClassPositionsOfMaximalNormalSubgroups', 739
  `ClassPositionsOfMinimalNormalSubgroups', 739
  `ClassPositionsOfNormalClosure', 740
  `ClassPositionsOfNormalSubgroup', 765
  `ClassPositionsOfNormalSubgroups', 739
  `ClassPositionsOfSupersolvableResiduum', 740
  `ClassPositionsOfUpperCentralSeries', 740
  `ClassRoots', 739
  `ClassStructureCharTable', 746
  `ClassTypesTom', 708
  `CleanedTailPcElement', 439
  `ClearCacheStats', 84
  `ClearProfile', 83
  clone, an object, 113
  `CloseMutableBasis', 606
  `CloseStream', 98
  `ClosureGroup', 353
  `ClosureGroupAddElm', 353
  `ClosureGroupCompare', 353
  `ClosureGroupDefault', 353
  `ClosureGroupIntest', 353
  `ClosureLeftModule', 574
  `ClosureNearAdditiveGroup', 560
  Closure Operations and Other Constructors, \indexit{316}
  `ClosureRing', 562
  Closures of (Sub)groups, \indexit{353}
  `Closure<Struct>', 288
  `ClosureSubgroup', 353
  `ClosureSubgroupNC', 353
  `Coboundaries', 656
  `Cochain', 655
  `CochainSpace', 655
  `Cocycles', 656
  cocycles, 379
  `CodePcGroup', 461
  `CodePcgs', 461
  Coding a Pc Presentation, \indexit{461}
  coefficient, binomial, 147
  Coefficient List Arithmetic, \indexit{217}
  `Coefficients', 602
  coefficients, for cyclotomics, 159
  `CoefficientsAndMagmaElements', 664
  `CoefficientsFamily', 687
  `CoefficientsMultiadic', 130
  `CoefficientsOfLaurentPolynomial', 679
  `CoefficientsOfUnivariatePolynomial', 672
  `Coefficients\-Of\-Univariate\-Rational\-Function', 672
  `CoefficientsQadic', 130
  `CoefficientsRing', 680
  `CoeffsCyc', 159
  `CoeffsMod', 218
  cohomology, 379
  `COHORTS_PRIMITIVE_GROUPS', 527
  `CoKernelOfAdditiveGeneralMapping', 311
  `CoKernelOfMultiplicativeGeneralMapping', 310
  `CollapsedMat', 816
  `Collected', 199
  Collection Families, \indexit{267}
  `CollectionsFamily', 267
  Coloring the Prompt and Input, \indexit{38}
  `ColorPrompt', 38
  `ColumnIndexOfReesMatrixSemigroupElement', 544
  `Column\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 544
  `Combinations', 149
  Combinations, Arrangements and Tuples, \indexit{149}
  `CombinatorialCollector', 455
  Combinatorial Numbers, \indexit{147}
  `Comm', 296
    \sub for words, 334
  Command Line Options, \indexit{27}
  comments, 41
  `CommutativeDiagram', 813
  `CommutatorFactorGroup', 372
  `CommutatorLength', 363
    \sub for character tables, 735
  `CommutatorSubgroup', 362
  `Compacted', 198
  `CompanionMat', 236
  `CompareVersionNumbers', 848
  comparison, fp semigroup elements, 550
    \sub operation, 295
    \sub rational functions, 670
  Comparison of Associative Words, \indexit{333}
  Comparison of Class Functions, \indexit{770}
  Comparison of Elements of Finitely Presented Groups, \indexit{464}
  Comparison of Elements of Finitely Presented Semigroups, \indexit{550}
  Comparison of Permutations, \indexit{412}
  Comparison of Rational Functions, \indexit{670}
  Comparison of Words, \indexit{327}
  Comparison Operations for Elements, \indexit{295}
  Comparisons, \indexit{47}
  comparisons, of booleans, 169
    \sub of lists, 183
  Comparisons of Booleans, \indexit{169}
  Comparisons of Cyclotomics, \indexit{161}
  Comparisons of Lists, \indexit{183}
  Comparisons of Records, \indexit{264}
  Comparisons of Strings, \indexit{253}
  `CompatibleConjugacyClasses', 732
  `CompatiblePairs', 459
  Compilation, \indexit{832}
  Compiling Library Code, \indexit{36}
  `Complementclasses', 362
  `ComplementclassesEA', 381
  `ComplementIntMat', 241
  `ComplementSystem', 365
  Completion Files, \indexit{34}
  `ComplexConjugate', 164
    \sub for class functions, 773
  `ComplexificationQuat', 618
  Components of a Dixon Record, \indexit{755}
  `CompositionMapping', 304
    \sub for Frobenius automorphisms, 588
  `CompositionMapping2', 304
  `CompositionMaps', 810
  `CompositionOfStraightLinePrograms', 341
  `CompositionSeries', 369
    \sub for groups with pcgs, 450
  `ComputedBrauerTables', 727
  `ComputedClassFusions', 806
  `ComputedIndicators', 745
  `ComputedIsPSolvableCharacterTables', 745
  `ComputedPowerMaps', 802
  `ComputedPrimeBlockss', 741
  Computing a Pcgs, \indexit{436}
  Computing a Permutation Representation, \indexit{416}
  Computing Pc Groups, \indexit{456}
  Computing Possible Permutation Characters, \indexit{795}
  Computing the Irreducible Characters of a Group, \indexit{750}
  `Concatenation', 198
  concatenation, of lists, 198
  `Conductor', 159
  `ConfluentRws', 345
  `Congruences', for character tables, 818
  Congruences for semigroups, \indexit{541}
  `ConjugacyClass', 359
  Conjugacy Classes, \indexit{359}
  `ConjugacyClasses', attribute, 359
    \sub for character tables, 731
    \sub for groups with pcgs, 450
    \sub for linear groups, 516
  `ConjugacyClassesByOrbits', 360
  `ConjugacyClassesByRandomSearch', 360
  Conjugacy Classes in Classical Groups, \indexit{516}
  Conjugacy Classes in Solvable Groups, \indexit{450}
  `ConjugacyClassesMaximalSubgroups', 373
  `ConjugacyClassesPerfectSubgroups', 376
  `ConjugacyClassesSubgroups', 373
  `ConjugacyClassSubgroups', 373
  conjugate, matrix, 224
    \sub of a word, 334
  `ConjugateDominantWeight', 648
  `ConjugateDominantWeightWithWord', 648
  `ConjugateGroup', 350
  `Conjugates', 581
  `ConjugateSubgroup', 352
  `ConjugateSubgroups', 352
  conjugation, 397
  `ConjugatorAutomorphism', 390
  `ConjugatorAutomorphismNC', 390
  `ConjugatorIsomorphism', 389
  `ConjugatorOfConjugatorIsomorphism', 390
  `ConnectGroupAndCharacterTable', 731
  `ConsiderKernels', 818
  `ConsiderSmallerPowerMaps', 819
  `ConsiderStructureConstants', 810
  `ConsiderTableAutomorphisms', 821
  `ConstantTimeAccessList', 194
  constituent, of a group character, 777
  `ConstituentsCompositionMapping', 305
  `ConstituentsOfCharacter', 778
  Constructing Algebras as Free Algebras, \indexit{615}
  Constructing Algebras by Generators, \indexit{614}
  Constructing Algebras by Structure Constants, \indexit{616}
  Constructing Character Tables from Others, \indexit{757}
  Constructing Domains, \indexit{287}
  Constructing Lie algebras, \indexit{640}
  Constructing Pc Groups, \indexit{454}
  Constructing Subdomains, \indexit{291}
  Constructing Tables of Marks, \indexit{703}
  Constructing Vector Spaces, \indexit{598}
  Construction of Abelian Number Fields, \indexit{591}
  Construction of Stabilizer Chains, \indexit{421}
  Constructors for Basic Groups, \indexit{516}
  `ContainedCharacters', 817
  `ContainedDecomposables', 817
  `ContainedMaps', 812
  `ContainedPossibleCharacters', 815, 816
  `ContainedPossibleVirtualCharacters', 815, 816
  `ContainedSpecialVectors', 815, 816
  `ContainedTom', 713
  `ContainingTom', 713
  `ContinuedFractionApproximationOfRoot', 143
  `ContinuedFractionExpansionOfRoot', 143
  Continued Fractions, \indexit{143}
  `continue' statement, 55
  Conventions for Character Tables, \indexit{730}
  convert, to a string, 252
  Converting Groups to Finitely Presented Groups, \indexit{472}
  `ConvertToCharacterTable', 729
  `ConvertToCharacterTableNC', 729
  `ConvertToMatrixRep', 236
  `ConvertToMatrixRepNC', 236
  `ConvertToRangeRep', 208
  `ConvertToStringRep', 252
  `ConvertToTableOfMarks', 707
  `ConvertToVectorRep', 216
  `ConvertToVectorRepNC', 216
  `ConwayPolynomial', 588
  Conway Polynomials, \indexit{588}
  coprime, 48
  copy, 113
    \sub an object, 113
  `COPY_LIST_ENTRIES', 178
  `CopyOptionsDefaults', 425
  Copyrights, \indexit{844}
  `CopyStabChain', 425
  `Core', 361
  `CorrespondingGeneratorsByModuloPcgs', 443
  coset, 356
  `CosetLeadersMatFFE', 219
  Cosets, \indexit{356}
  `CosetTable', 466
  `CosetTableBySubgroup', 467
  `CosetTableDefaultLimit', 468
  `CosetTableDefaultMaxLimit', 468
  `CosetTableFromGensAndRels', 467
  `CosetTableInWholeGroup', 470
  `CosetTableOfFpSemigroup', 553
  Coset Tables and Coset Enumeration, \indexit{466}
  Coset tables for subgroups in the whole group, \indexit{470}
  `CosetTableStandard', 469
  CRC, 37
  `CrcFile', 95
    \sub example, 37
  CRC Numbers, \indexit{37}
  `CreateCompletionFiles', 34
  `CreateCompletionFilesPkg', 849
  Creating Character Tables, \indexit{726}
  Creating Class Functions from Values Lists, \indexit{774}
  Creating Class Functions using Groups, \indexit{775}
  Creating Finite Fields, \indexit{586}
  Creating Finitely Presented Groups, \indexit{463}
  Creating Finitely Presented Semigroups, \indexit{549}
  Creating Group Homomorphisms, \indexit{384}
  Creating Groups, \indexit{349}
  Creating Mappings, \indexit{304}
  Creating Permutations, \indexit{414}
  Creating Presentations, \indexit{481}
  Creation of Algebraic Extensions, \indexit{691}
  Creation of Rational Functions, \indexit{689}
  Credit, \indexit{21}
  `CrystGroupDefaultAction', 434
  `Cycle', 405
  `CycleLength', 405
  `CycleLengths', 405
  `Cycles', 405
  `CycleStructureClass', 779
  `CycleStructurePerm', 413
  `CyclicExtensionsTom', 713
  `CyclicGroup', 510
  `CyclotomicField', 591
  cyclotomic field elements, 157
  cyclotomic fields, canonicalbasis, 594
  `CyclotomicPolynomial', 676
  Cyclotomic Polynomials, \indexit{676}
  `Cyclotomics', 157
  cyclotomics, defaultfield, 592
\letter D
  $d_N$, 161
  Darstellungsgruppe, see `EpimorphismSchurCover', 382
  `DataType', 125
  data type, unknown, 167
  `DayDMY', 259
  `DaysInMonth', 258
  `DaysInYear', 258
  Debugging Recursion, \indexit{85}
  DEC, 244
  `DeclareAutoPackage', 849
  `DeclareHandlingByNiceBasis', 612
  `DeclareInfoClass', 80
  `DeclarePackage', 849
  `DeclarePackageAutoDocumentation', 849
  `DeclarePackageDocumentation', 849
  `DecodeTree', 499
  DecodeTree, \indexit{499}
  decompose, a group character, 777
  `DecomposedFixedPointVector', 713
  `DecomposeTensorProduct', 657
  `Decomposition', 244
  `DecompositionInt', 245
  `DecompositionMatrix', 743
  decomposition matrix, 244
  Decompositions, \indexit{244}
  `Decreased', 786
  `DefaultField', 578
    \sub for cyclotomics, 160
    \sub for finite field elements, 586
  `DefaultFieldByGenerators', 578
  `DefaultFieldOfMatrix', 225
  `DefaultFieldOfMatrixGroup', 429
  `DefaultRing', 561
    \sub for finite field elements, 586
  `DefaultRingByGenerators', 562
  `DefaultStabChainOptions', 422
  Defining a Pcgs Yourself, \indexit{436}
  `DefiningPolynomial', 579
  `DefiningQuotientHomomorphism', 476
  `DegreeFFE', 585
  `DegreeIndeterminate', 674
  `DegreeOfBinaryRelation', 315
  `DegreeOfCharacter', 777
  `DegreeOfLaurentPolynomial', 673
  `DegreeOfTransformation', 554
  `DegreeOfTransformationSemigroup', 540
  `DegreeOverPrimeField', 579
  `Delta', 824
  denominator, of a rational, 146
  `DenominatorCyc', 160
  `DenominatorOfModuloPcgs', 442
  `DenominatorOfRationalFunction', 672
  `DenominatorRat', 146
  deprecated, 849
  `DepthOfPcElement', 438
  `DepthOfUpperTriangularMatrix', 234
  `Derangements', 151
  `Derivations', 641
  `Derivative', 675
  `DerivedLength', 370
  `DerivedSeriesOfGroup', 370
  `DerivedSubgroup', 362
  `DerivedSubgroupsTom', 712
  `DerivedSubgroupsTomPossible', 712
  `DerivedSubgroupsTomUnique', 712
  `DerivedSubgroupTom', 712
  `DescriptionOfRootOfUnity', 160
  `Determinant', 226
  determinant character, 780
  `DeterminantIntMat', 244
  `DeterminantMat', 226
  `DeterminantMatDestructive', 226
  `DeterminantMatDivFree', 226
  Determinant of an integer matrix, \indexit{244}
  `DeterminantOfCharacter', 780
  Developing rewriting systems, \indexit{347}
  `DiagonalizeIntMat', 242
  `DiagonalizeMat', 231
  `DiagonalMat', 227
  `DiagonalOfMat', 234
  `Difference', 275
  `DifferenceBlist', 211
  `DihedralGroup', 511
  `Dimension', 575
  `DimensionOfHighestWeightModule', 657
  `DimensionOfMatrixGroup', 429
  `DimensionOfVectors', 607
  `DimensionsLoewyFactors', 371
  `DimensionsMat', 225
  Directories, \indexit{91}
  `DirectoriesLibrary', 91
  `DirectoriesPackageLibrary', 847
  `DirectoriesPackagePrograms', 848
  `DirectoriesSystemPrograms', 92
  `Directory', 91
  `DirectoryContents', 92
  `DirectoryCurrent', 91
  `DirectoryTemporary', 91
  `DirectProduct', 504
  `DirectProductOp', 504
  Direct Products, \indexit{504}
  `DirectSumDecomposition', 626
    \sub for Lie algebras, 645
  Direct Sum Decompositions, \indexit{645}
  `DirectSumOfAlgebraModules', 637
    \sub for Lie algebras, 660
  `DirectSumOfAlgebras', 625
  `DisableAttributeValueStoring', 123
  disable automatic loading, 845
  `Discriminant', 675
  `Display', 67
    \sub for character tables, 747, 774
    \sub for tables of marks, 705
  `DisplayCacheStats', 84
  `DisplayCompositionSeries', 369
  `DisplayEggBoxOfDClass', 542
  `DisplayImfInvariants', 531
  `DisplayInformationPerfectGroups', 524
  `DisplayOptions', 749
  `DisplayOptionsStack', 89
  `DisplayProfile', 83
  `DisplayRevision', 84
  `DistancesDistributionMatFFEVecFFE', 219
  `DistancesDistributionVecFFEsVecFFE', 219
  `DistanceVecFFE', 219
  Distinguished Subalgebras, \indexit{642}
  division, 48
    \sub operation, 296
  `DivisionRingByGenerators', 578
  division rings, 577
  divisors, of an integer, 134
  `DivisorsInt', 134
  Dixon-Schneider algorithm, 753
  `DixonInit', 754
  `DixonRecord', 754
  `DixonSplit', 754
  `DixontinI', 754
  `DMYDay', 259
  `DMYhmsSeconds', 260
  `DnLattice', 787
  `DnLatticeIterative', 788
  `do', 53
  document formats (text, dvi, ps, pdf, html), 23
  `Domain', 292
  `DomainByGenerators', 292
  Domain Categories, \indexit{289}
  Domains, \indexit{110}
  Domains Generated by Class Functions, \indexit{800}
  Domains of Subspaces of Vector Spaces, \indexit{600}
  `DominantCharacter', 656
  `DominantWeights', 656
  `DoubleCoset', 358
  `DoubleCosetRepsAndSizes', 359
  Double Cosets, \indexit{358}
  `DoubleCosets', operation, 358
  `DoubleCosetsNC', operation, 358
  doublequote character, 251
  doublequotes, 249
  `DownEnv', 71
  Dummy Streams, \indexit{106}
  duplicate free, 194
  `DuplicateFreeList', 199
  Duplication of Lists, \indexit{180}
  Duplication of Objects, \indexit{113}
  `DxIncludeIrreducibles', 754
\letter E
  `E', 157
  $e_N$, 161
  `EANormalSeriesByPcgs', 444
  `Earns', 406
  `EB', 161
  `EC', 161
  Echelonized Matrices, \indexit{231}
  `ED', 161
  `Edit', 75
  Editing Files, \indexit{75}
  Editor Support, \indexit{75}
  `EE', 161
  `EF', 161
  Efficiency of Homomorphisms, \indexit{387}
  `EG', 161
  `EggBoxOfDClass', 542
  `EH', 161
  `EI', 162
  `Eigenspaces', 230
  `Eigenvalues', 230
  `EigenvaluesChar', 780
  `Eigenvectors', 230
  Eigenvectors and eigenvalues, \indexit{230}
  `EJ', 162
  `EK', 162
  `EL', 162
  `ElementaryAbelianGroup', 511
  `ElementaryAbelianSeries', 370
  `ElementaryAbelianSeriesLargeSteps', 370
  Elementary Divisors, \indexit{231}
  `ElementaryDivisorsMat', 231
  `ElementaryDivisorsMatDestructive', 231
  Elementary Operations for a Pcgs, \indexit{437}
  Elementary Operations for a Pcgs and an Element, \indexit{438}
  Elementary Operations for Integers, \indexit{127}
  Elementary Operations for Rationals, \indexit{145}
  Elementary Tietze Transformations, \indexit{492}
  `ElementOfFpGroup', 465
  `ElementOfFpSemigroup', 551
  `ElementOfMagmaRing', 664
  `ElementOrdersPowerMap', 803
  `ElementProperty', 426
  `Elements', 272
  elements, definition, 109
    \sub of a list or collection, 272
  Elements as equivalence classes, \indexit{109}
  `ElementsFamily', 267
  Elements in Algebraic Extensions, \indexit{691}
  Elements of Free Magma Rings, \indexit{664}
  Elements of pc groups, \indexit{453}
  `ElementsStabChain', 424
  Elements with Prescribed Images, \indexit{402}
  element test, for lists, 182
  `elif', 51
  `EliminatedWord', 335
  `EliminationOrdering', 684
  `else', 51
  `EM', 162
  `emacs', 75
  `Embedding', 305
    \sub example for direct products, 504
    \sub example for semidirect products, 506
    \sub example for wreath products, 507
    \sub for group products, 509
    \sub for Lie algebras, 640
    \sub for magma rings, 664
  embeddings, find all, 393
  Embeddings and Projections for Group Products, \indexit{509}
  `EmptyBinaryRelation', 314
  `EmptyMatrix', 227
  `EmptyPlist', 182
  `EmptySCTable', 616
  `EmptyStabChain', 425
  `EmptyString', 252
  `EnableAttributeValueStoring', 123
  `End', 610
  `end', 55
  Enlarging Internally Represented Lists, \indexit{182}
  `Enumerator', 268
  `EnumeratorByBasis', 603
  `EnumeratorByFunctions', 269
  Enumerators, \indexit{208}
  `EnumeratorSorted', 268
  environment, 55
  `Epicentre', 382
  `EpimorphismFromFreeGroup', 353
  `EpimorphismNilpotentQuotient', 477
  `EpimorphismNonabelianExteriorSquare', 382
  `EpimorphismPGroup', 477
  `EpimorphismQuotientSystem', 477
  epimorphisms, find all, 393
  `EpimorphismSchurCover', 382
  equality, associative words, 333
    \sub elements of finitely presented groups, 464
    \sub nonassociative words, 327
    \sub of records, 264
    \sub operation, 295
    \sub pcwords, 453
  Equality and Comparison of Domains, \indexit{287}
  equality test, 47
    \sub for permutations, 412
  equivalence class, 318
  Equivalence Classes, \indexit{318}
  `EquivalenceClasses', attribute, 318
  `EquivalenceClassOfElement', 318
  `EquivalenceClassOfElementNC', 318
  `EquivalenceClassRelation', 318
  equivalence relation, 315, 317
  `EquivalenceRelationByPairs', 317
  `EquivalenceRelationByPairsNC', 317
  `EquivalenceRelationByPartition', 317
  `EquivalenceRelationByPartitionNC', 317
  `EquivalenceRelationByProperty', 317
  `EquivalenceRelationByRelation', 317
  `EquivalenceRelationPartition', 317
  Equivalence Relations, \indexit{317}
  `ER', 162
  `Error', 73
  Error, \indexit{73}
  `ErrorCount', 73
  ErrorCount, \indexit{73}
  `ErrorNoTraceBack', 69
  errors, syntax, 64
  `ES', 162
  escaped characters, 251
  escaping non-special characters, 251
  `ET', 162
  `EU', 162
  `EuclideanDegree', 569
  `EuclideanQuotient', 569
  `EuclideanRemainder', 570
  Euclidean Rings, \indexit{569}
  Euler's totient function, 138
  `EulerianFunction', 368
  `EulerianFunctionByTom', 714
  `EV', 162
  `EvalStraightLineProgElm', 343
  `EvalString', 258
  evaluation, 42
    \sub strings, 257
  `EW', 162
  `EX', 162
  `ExactSizeConsiderFunction', 378
  `Exec', 108
  Exec, \indexit{108}
  execution, 49
  exit, 73
  expanded form of monomials, 688
  Expert Windows installation, \indexit{843}
  `Exponent', 368
    \sub for character tables, 735
  exponent, of the prime residue group, 139
  exponentiation, operation, 296
  `ExponentOfPcElement', 438
  `ExponentsConjugateLayer', 439
  `ExponentsOfCommutator', 439
  `ExponentsOfConjugate', 439
  `ExponentsOfPcElement', 438
  `ExponentsOfRelativePower', 439
  Exponents of Special Products, \indexit{439}
  `ExponentSumWord', 334
  `ExponentSyllable', 336
  Expressing Group Elements as Words in Generators, \indexit{353}
  Expressions, \indexit{42}
  `ExtendedPcgs', 441
  `ExtendStabChain', 425
  `Extension', 458
  `ExtensionNC', 458
  `ExtensionRepresentatives', 459
  `Extensions', 458
  Extensions of the p-adic Numbers, \indexit{694}
  `ExteriorCentre', 382
  `ExteriorPowerOfAlgebraModule', 660
  `ExternalOrbit', 409
  `ExternalOrbits', 409
  `ExternalOrbitsStabilizers', 409
  External Representation for Nonassociative Words, \indexit{329}
  external representation of polynomials, 688
  `ExternalSet', 408
  External Sets, \indexit{408}
  `ExternalSubset', 409
  `Extract', 784
  `ExtraspecialGroup', 511
  `ExtRepDenominatorRatFun', 688
  `ExtRepNumeratorRatFun', 688
  `ExtRepOfObj', external representation, for cyclotomics, 160
  `ExtRepPolynomialRatFun', 688
  `EY', 162
\letter F
  $f_N$, 161
  `FactorCosetAction', 404
    \sub for fp groups, 467
  `FactorCosetOperation', 467
  `FactorFreeSemigroupByRelations', 549
  `FactorGroup', 372
  `FactorGroupFpGroupByRels', 463
  `FactorGroupNC', 372
  `FactorGroupNormalSubgroupClasses', 765
  Factor Groups, \indexit{372}
  Factor Groups of Polycyclic Groups - Modulo Pcgs, \indexit{442}
  Factor Groups of Polycyclic Groups in their Own Representation, \indexit{443}
  `FactorGroupTom', 714
  `Factorial', 147
  `Factorization', 354
  factorization, 353
  `Factors', 569
    \sub of univariate polynomial, 677
  `FactorsInt', 132
  `FactorsOfDirectProduct', 758
  `FactorsSquarefree', 677
  Fail, \indexit{169}
  `fail', 169
  `FaithfulModule', 636
    \sub for Lie algebras, 654
  Families, \indexit{116}
  `FamiliesOfGeneralMappingsAndRanges', 313
  `FamiliesOfRows', 764
  `FamilyForOrdering', 281
  `FamilyObj', 116
  `FamilyPcgs', 453
  `FamilyRange', 313
  `FamilySource', 313
  FAQ, 836
  features, under UNIX, 27
  `fi', 51
  `Fibonacci', 155
  Fibonacci and Lucas Sequences, \indexit{155}
  `Field', 577
  `FieldExtension', 579
  field homomorphisms, Frobenius, 588
  `FieldOfMatrixGroup', 429
  `FieldOverItselfByGenerators', 579
  fields, 577
  File Access, \indexit{93}
  `FileDescriptorOfStream', 98
  `Filename', 92
  Filename, \indexit{92}
  File Operations, \indexit{94}
  File Streams, \indexit{103}
  `Filtered', 202
  Filters, \indexit{117}
  Filters Controlling the Arithmetic Behaviour of Lists, \indexit{184}
  Finding Positions in Lists, \indexit{190}
  Finding Submodules, \indexit{697}
  `FindSl2', 652
  Finish Installation and Cleanup, \indexit{834}
  Finite Field Elements, \indexit{583}
  Finitely Presented Lie Algebras, \indexit{652}
  Finitely presented monoids, \indexit{551}
  finiteness test, for a list or collection, 272
  Finite Perfect Groups, \indexit{522}
  `First', 203
  `FittingSubgroup', 363
  `Flat', 199
  flush character, 251
  For, \indexit{53}
  `ForAll', 203
  `ForAny', 203
  `for' loop, 53
  `FpElmComparisonMethod', 464
  `FpGroupPresentation', 482
  `FpGrpMonSmgOfFpGrpMonSmgElement', 549
  `FpLieAlgebraByCartanMatrix', 653
  frame, 789, 790
  `FrattiniSubgroup', 363
    \sub for groups with pcgs, 450
  `FreeAlgebra', 615
  `FreeAlgebraWithOne', 615
  `FreeAssociativeAlgebra', 615
  `FreeAssociativeAlgebraWithOne', 615
  `FreeGeneratorsOfFpGroup', 464
  `FreeGeneratorsOfFpSemigroup', 550
  `FreeGeneratorsOfWholeGroup', 464
  `FreeGroup', 331
  `FreeGroupOfFpGroup', 464
  Free Groups, Monoids and Semigroups, \indexit{331}
  `FreeLeftModule', 575
  `FreeLieAlgebra', 641
  `FreeMagma', 328
  `FreeMagmaRing', 663
  Free Magma Rings, \indexit{663}
  Free Magmas, \indexit{328}
  `FreeMagmaWithOne', 328
  Free Modules, \indexit{575}
  `FreeMonoid', 546
    \sub with example, 331
  `FreeMonoidOfRewritingSystem', 553
  `FreeProduct', 509
  Free Products, \indexit{509}
  `FreeSemigroup', 331
    \sub with examples, 539
  `FreeSemigroupOfFpSemigroup', 550
  `FreeSemigroupOfRewritingSystem', 553
  Frobenius automorphism, 588
  `FrobeniusAutomorphism', 588
  FrobeniusAutomorphism, \indexit{588}
  `FrobeniusCharacterValue', 799
  `FullMatrixAlgebra', 618
  `FullMatrixAlgebraCentralizer', 626
  `FullMatrixLieAlgebra', 641
  `FullMatrixModule', 576
  `FullMatrixSpace', 607
  `FullRowModule', 576
  `FullRowSpace', 607
  `FullTransformationSemigroup', 540
  Function, \indexit{55}
  `function', 55
  `FunctionAction', 408
  function call, 46
    \sub with arguments, 46
    \sub with options, 47
  Function Calls, \indexit{46}
  `FunctionOperation', 849
  functions, 61, 303
    \sub definition by arrow notation, 57
    \sub definition of, 55
    \sub recursive, 55
    \sub with a variable number of arguments, 46, 56
  `FunctionsFamily', 63
  Functions for Coding Theory, \indexit{219}
  Functions for GAP Packages, \indexit{846}
  Functions that do nothing, \indexit{63}
  Function that Modify Boolean Lists, \indexit{212}
  Function Types, \indexit{63}
  `FusionCharTableTom', 720
  `FusionConjugacyClasses', 806
  `FusionConjugacyClassesOp', 806
  fusions, 805
  `FusionsAllowedByRestrictions', 821
  `FusionsTom', 709
\letter G
  $G$-sets, 396, 408
  $g_N$, 161
  `gac', 35
  Galois Action, \indexit{579}
  Galois Conjugacy of Cyclotomics, \indexit{164}
  `GaloisCyc', 164
    \sub for class functions, 773
  `GaloisField', 587
  `GaloisGroup', of field, 580
    \sub of rational class of a group, 361
  Galois Groups of Abelian Number Fields, \indexit{596}
  `GaloisMat', 165
  `GaloisStabilizer', 593
  `GaloisType', 678
  `gap.rc', 32, 33
  GAP3, 34
  `Gap3CatalogueIdGroup', 520
  GAP for Macintosh OS X, \indexit{840}
  GAP for MacOS, \indexit{841}
  `GAPInfo', 850
  `GAPInfo.RootPaths', 29
  `GapInputPcGroup', 457
  `GapInputSCTable', 616
  `GAPKB_REW', 552
  GAP Root Directory, \indexit{90}
  `GasmanLimits', 87
  `GasmanMessageStatus', 87
  `GasmanStatistics', 87
  Gaussian algorithm, 229
  `GaussianIntegers', 597
  `GaussianRationals', 592
  Gaussians, \indexit{597}
  `Gcd', 570
  Gcd and Lcm, \indexit{570}
  `Gcdex', 130
  `GcdInt', 129
  `GcdOp', 570
  `GcdRepresentation', 570
  `GcdRepresentationOp', 571
  General Binary Relations, \indexit{314}
  `GeneralisedEigenspaces', 230
  `GeneralisedEigenvalues', 230
  generalized characters, 767
  `GeneralizedEigenspaces', 230
  `GeneralizedEigenvalues', 230
  `GeneralLinearGroup', 513
  `GeneralMappingByElements', 304
  General Mappings, \indexit{312}
  `GeneralMappingsFamily', 313
  `GeneralOrthogonalGroup', 514
  `GeneralUnitaryGroup', 513
  Generating Fields, \indexit{577}
  Generating modules, \indexit{573}
  Generating Rings, \indexit{561}
  generator, of the prime residue group, 140
  `GeneratorsOfAdditiveGroup', 559
  `GeneratorsOfAdditiveMagma', 559
  `GeneratorsOfAdditiveMagmaWithZero', 559
  `GeneratorsOfAlgebra', 622
  `GeneratorsOfAlgebraModule', 633
  `GeneratorsOfAlgebraWithOne', 622
  `GeneratorsOfDivisionRing', 578
  `GeneratorsOfDomain', 292
  `Generators\-Of\-Equivalence\-Relation\-Partition', 317
  `GeneratorsOfField', 578
  `GeneratorsOfGroup', 350
  `GeneratorsOfIdeal', 564
  `GeneratorsOfLeftIdeal', 565
  `GeneratorsOfLeftModule', 573
  `GeneratorsOfLeftOperatorAdditiveGroup', 573
  `GeneratorsOfLeftVectorSpace', 599
  `GeneratorsOfMagma', 322
  `GeneratorsOfMagmaWithInverses', 322
  `GeneratorsOfMagmaWithOne', 322
  `GeneratorsOfMonoid', 545
  `GeneratorsOfNearAdditiveGroup', 559
  `GeneratorsOfNearAdditiveMagma', 559
  `GeneratorsOfNearAdditiveMagmaWithZero', 559
  `GeneratorsOfPresentation', 481
  `GeneratorsOfRightIdeal', 565
  `GeneratorsOfRightModule', 574
  `GeneratorsOfRightOperatorAdditiveGroup', 574
  `GeneratorsOfRing', 562
  `GeneratorsOfRingWithOne', 566
  `GeneratorsOfRws', 345
  `GeneratorsOfSemigroup', 539
  `GeneratorsOf<Struct>', 288
  `GeneratorsOfTwoSidedIdeal', 564
  `GeneratorsOfVectorSpace', 599
  `GeneratorsPrimeResidues', 139
  `GeneratorsSmallest', 379
  `GeneratorsSubgroupsTom', 718
  `GeneratorSyllable', 336
  Generic Construction of Tables of Marks, \indexit{722}
  `GetFusionMap', 807
  Get the Archives, \indexit{831}
  getting help, 22
  `GF', 587
  `GL', 513
  GL and SL, \indexit{430}
  Global Memory Information, \indexit{87}
  `GlobalMersenneTwister', 136
  `GlobalRandomSource', 136
  `GModuleByMats', 696
  `GO', 514
  `GQuotients', 393
  `Grading', 627
  Green's Relations, \indexit{541}
  `GreensDClasses', 543
  `GreensDClassOfElement', 542
  `GreensDRelation', 542
  `GreensHClasses', 543
  `GreensHClassOfElement', 542
  `GreensHRelation', 542
  `GreensJClasses', 543
  `GreensJClassOfElement', 542
  `GreensJRelation', 542
  `GreensLClasses', 543
  `GreensLClassOfElement', 542
  `GreensLRelation', 542
  `GreensRClasses', 543
  `GreensRClassOfElement', 542
  `GreensRRelation', 542
  Groebner Bases, \indexit{685}
  `GroebnerBasis', 685
  `GroebnerBasisNC', 685
  `Group', 349
  group actions, 396, 397
    \sub operations syntax, 396
  Group Actions - Name Changes, \indexit{849}
  group algebra, 662
  Group Automorphisms, \indexit{389}
  `GroupByRws', 455
  `GroupByRwsNC', 455
  group characters, 767
  Group Elements, \indexit{349}
  `GroupGeneralMappingByImages', 385
  `GroupHClassOfGreensDClass', 543
  `GroupHomomorphismByFunction', 385
  `GroupHomomorphismByImages', 384
  `GroupHomomorphismByImagesNC', 384
  `GroupOfPcgs', 437
  group operations, 397, 849
  Group Properties, \indexit{366}
  `GroupRing', 663
  group ring, 662
  Groups of Automorphisms, \indexit{391}
  `GroupStabChain', 424
  `GroupWithGenerators', 350
  `GU', 513
\letter H
  $h_N$, 161
  `HallSubgroup', 364
  `HallSystem', 365
    \sub for groups with pcgs, 450
  Handling of Streams in the Background, \indexit{106}
  `HasAbelianFactorGroup', 372
  `HasElementaryAbelianFactorGroup', 372
  `HasIndeterminateName', 669
  `HasParent', 290
  `HasseDiagramBinaryRelation', 316
  `HeadPcElementByNumber', 439
  `HenselBound', 678
  hermite normal form, 850
  `HermiteNormalFormIntegerMat', 242
  `HermiteNormalFormIntegerMatTransform', 242
  `HeuristicCancelPolynomials', 690
  `HexStringInt', 254
  `HighestWeightModule', 659
  History of Character Theory Stuff in GAP, \indexit{725}
  `HMSMSec', 259
  `Hom', 610
  `HomeEnumerator', 408
  Homomorphism for very large groups, \indexit{388}
  `HomomorphismQuotientSemigroup', 541
  homomorphisms, find all, 393
  homomorphisms, Frobenius, field, 588
  Homomorphisms of Algebras, \indexit{628}
  `HomomorphismTransformationSemigroup', 540
  How to Implement New Kinds of Vector Spaces, \indexit{612}
  `HumanReadableDefinition', 716
\letter I
  $i_N$, 162
  `Ideal', 563
  `IdealByGenerators', 564
  `IdealNC', 564
  Ideals, \indexit{620}
  Ideals in Rings, \indexit{563}
  Ideals of semigroups, \indexit{540}
  `Idempotents', 323
  `IdempotentsTom', 709
  `IdempotentsTomInfo', 709
  Identical Lists, \indexit{179}
  Identical Objects, \indexit{110}
  Identical Records, \indexit{263}
  `IdentificationOfConjugacyClasses', 731
  `Identifier', for character tables, 738
    \sub for tables of marks, 710
  Identifiers, \indexit{42}
  `Identity', 292
  `IdentityBinaryRelation', 314
  `IdentityFromSCTable', 617
  `IdentityMapping', 305
  `IdentityMat', 227
  `IdentityTransformation', 554
  `IdFunc', 63
  `IdGap3SolvableGroup', 520
  `IdGroup', 520
  `IdSmallGroup', 520
  `IdsOfAllSmallGroups', 520
  If, \indexit{51}
  `if' statement, 51
  If Things Go Wrong, \indexit{836}
  `Image', 307
    \sub for Frobenius automorphisms, 588
  image, vector under matrix, 224
  `ImageElm', 307
  `ImageListOfTransformation', 555
  `Images', 307
  `ImagesElm', 306
  `ImageSetOfTransformation', 555
  `ImagesRepresentative', 306
  `ImagesSet', 306
  `ImagesSmallestGenerators', 388
  `ImagesSource', 306
  Images under Mappings, \indexit{306}
  `ImfInvariants', 533
  `ImfMatrixGroup', 534
  `ImfNumberQClasses', 531
  `ImfNumberQQClasses', 531
  `ImfNumberZClasses', 531
  `Immutable', 112
  `ImmutableBasis', 606
  `ImmutableMatrix', 236
  `in', for collections, 276
    \sub for lists, 182
    \sub for strictly sorted lists, 196
    \sub operation for, 276
  `IndependentGeneratorsOfAbelianGroup', 379
  `Indeterminate', 668
  `IndeterminateName', 669
  `Indeterminateness', 815
  `IndeterminateNumberOfLaurentPolynomial', 679
  `Indeterminate\-Number\-Of\-Univariate\-Rational\-Function', 669
  `Indeterminate\-Of\-Univariate\-Rational\-Function', 669
  Indeterminates, \indexit{668}
  `IndeterminatesOfPolynomialRing', 680
  `Index', 351
  `IndexInWholeGroup', 351
  `IndexNC', 351
  Index numbers of primitive groups, \indexit{528}
  `Indicator', 745
  `IndicatorOp', 745
  `IndicesCentralNormalSteps', 444
  `IndicesChiefNormalSteps', 445
  `IndicesEANormalSteps', 444
  `IndicesInvolutaryGenerators', 469
  `IndicesNormalSteps', 446
  `IndicesOfAdjointBasis', 623
  `IndicesPCentralNormalStepsPGroup', 445
  `IndicesStabChain', 424
  `Indirected', 811
  Induced Actions, \indexit{698}
  `InducedAutomorphism', 392
  `InducedClassFunction', 781
  `InducedClassFunctions', 782
  `InducedCyclic', 782
  `InducedPcgs', 440
  `InducedPcgsByGenerators', 440
  `InducedPcgsByGeneratorsNC', 440
  `InducedPcgsByPcSequence', 440
  `InducedPcgsByPcSequenceAndGenerators', 441
  `InducedPcgsByPcSequenceNC', 440
  `InducedPcgsWrtFamilyPcgs', 453
  `InducedPcgsWrtSpecialPcgs', 448
  `Inequalities', 798
  inequality, of records, 264
  inequality test, 47
  `InertiaSubgroup', 779
  Infinity, \indexit{160}
  `infinity', 160
  inflated class functions, 781
  `Info', 80
  `InfoAlgebra', 614
  `InfoAttributes', 123
  `InfoBckt', 426
  `InfoCharacterTable', 730
  `InfoCoh', 381
  `InfoComplement', 362
  `InfoCoset', 359
  `InfoFpGroup', 463
  Info Functions, \indexit{80}
  `InfoGroebner', 686
  `InfoGroup', 350
  `InfoLattice', 376
  `InfoLevel', 80
  `InfoMatrix', 222
  `InfoMonomial', 823
  `InfoNumtheor', 138
  `InfoOptions', 89
  `InfoPcSubgroup', 379
  Information about a function, \indexit{61}
  Information about the version used, \indexit{84}
  `InfoText', 738
  `InfoTom', 707
  `InfoWarning', 81
  `Init', 136
  `InitFusion', 820
  `InitPowerMap', 818
  `InjectionZeroMagma', 321
  `InnerAutomorphism', 390
  `InnerAutomorphismNC', 390
  `InnerAutomorphismsAutomorphismGroup', 391
  inner product, of group characters, 777
  Input-Output Streams, \indexit{104}
  `InputLogTo', 95
    \sub for streams, 102
    \sub stop logging input, 95
  `InputOutputLocalProcess', 105
  `InputTextFile', 103
  `InputTextNone', 106
  `InputTextString', 104
  `InputTextUser', 103
  `InsertTrivialStabilizer', 425
  `InstallAtExit', 73
  installation, 830
  Installation of GAP for MacOS, \indexit{841}
  Installation Overview, \indexit{830}
  `InstallCharReadHookFunc', 106
  `InstalledPackageVersion', 847
  `InstallFactorMaintenance', 298
  `InstallHandlingByNiceBasis', 612
  Installing a GAP Package, \indexit{845}
  `InstallIsomorphismMaintenance', 298
  `InstallSubsetMaintenance', 298
  `Int', 127
    \sub for cyclotomics, 158
    \sub for strings, 257
  `INT_CHAR', 257
  integer part of a quotient, 129
  `Integers', 126
  Integral Bases of Abelian Number Fields, \indexit{594}
  `IntegralizedMat', 245
  `IntegratedStraightLineProgram', 341
  `IntermediateGroup', 371
  `IntermediateResultOfSLP', 342
  `IntermediateResultOfSLPWithoutOverwrite', 342
  `Intermediate\-Results\-Of\-SLPWithout\-Overwrite', 342
  `IntermediateSubgroups', 371
  Internally Represented Cyclotomics, \indexit{166}
  Internally Represented Strings, \indexit{252}
  `InterpolatedPolynomial', 572
  `IntersectBlist', 212
  `Intersection', 274
    \sub for groups with pcgs, 450
  intersection, of collections, 274
    \sub of sets, 197
  `Intersection2', 274
  `IntersectionBlist', 211
  `IntersectionsTom', 714
  `IntersectSet', 197
  `IntFFE', 586
  `IntFFESymm', 586
  `IntHexString', 257
  `IntScalarProducts', 815, 816
  `IntVecFFE', 586
  `InvariantBilinearForm', 431
  `InvariantElementaryAbelianSeries', 370
  Invariant Forms, \indexit{431}, \indexit{699}
  `InvariantLattice', 433
  `InvariantQuadraticForm', 431
  `InvariantSesquilinearForm', 431
  `Invariant\-Subgroups\-Elementary\-Abelian\-Group', 377
  `Inverse', 294
  inverse, group homomorphism, 386
    \sub matrix, 224
    \sub of class function, 772
  `InverseAttr', 294
  `InverseClasses', 738
  `InverseGeneralMapping', 304
  `InverseImmutable', 294
  `InverseMap', 811
  `InverseMatMod', 238
  `InverseMutable', 294
  `InverseOp', 294
  `InverseRepresentative', 424
  `InverseSameMutability', 294
  `InverseSM', 294
  Invoking the Help, \indexit{22}
  `Irr', 734
  irrationalities, 157
  `IrrBaumClausen', 751
  `IrrConlon', 751
  `IrrDixonSchneider', 751
  Irreducibility Tests, \indexit{697}
  irreducible character, 776
  irreducible characters, computation, 754
  `IrreducibleDifferences', 783
  Irreducible Maximal Finite Integral Matrix Groups, \indexit{530}
  `IrreducibleModules', 753
    \sub for groups with pcgs, 450
  `IrreducibleRepresentations', 751
  `IrreducibleRepresentationsDixon', 752
  `IrreducibleSolvableGroup', 529
  `IrreducibleSolvableGroupMS', 529
  Irreducible Solvable Matrix Groups, \indexit{529}
  `Is16BitsFamily', 337
  `Is32BitsFamily', 337
  `Is8BitsFamily', 337
  `IsAbelian', 323
    \sub for character tables, 735
  `IsAbelianNumberField', 593
  `IsAbelianNumberFieldPolynomialRing', 681
  `IsAbelianTom', 711
  `IsAdditiveElement', 299
  `IsAdditiveElementWithInverse', 299
  `IsAdditiveElementWithZero', 299
  `IsAdditiveGroup', 558
  `IsAdditiveGroupGeneralMapping', 311
  `IsAdditiveGroupHomomorphism', 311
  `IsAdditivelyCommutative', 559
  `IsAdditivelyCommutativeElement', 301
  `IsAdditivelyCommutativeElementCollColl', 301
  `Is\-Additively\-Commutative\-Element\-Collection', 301
  `IsAdditivelyCommutativeElementFamily', 301
  `IsAdditiveMagma', 557
  `IsAdditiveMagmaWithInverses', 558
  `IsAdditiveMagmaWithZero', 557
  `IsAlgebra', 621
  `IsAlgebraGeneralMapping', 312
  `IsAlgebraHomomorphism', 312
  `IsAlgebraicElement', 692
  `IsAlgebraicExtension', 691
  `IsAlgebraModuleElement', 633
  `IsAlgebraModuleElementCollection', 633
  `IsAlgebraModuleElementFamily', 633
  `IsAlgebraWithOne', 621
  `IsAlgebraWithOneGeneralMapping', 312
  `IsAlgebraWithOneHomomorphism', 312
  `IsAlphaChar', 253
  `IsAlternatingGroup', 417
  `IsAnticommutative', 567
  `IsAntisymmetricBinaryRelation', 315
  `IsAssociated', 568
  `IsAssociative', 323
  `IsAssociativeElement', 301
  `IsAssociativeElementCollColl', 301
  `IsAssociativeElementCollection', 301
  `IsAssocWord', 330
  `IsAssocWordWithInverse', 330
  `IsAssocWordWithOne', 330
  `IsAutomorphismGroup', 391
  `IsBasicWreathLessThanOrEqual', 333
  `IsBasicWreathProductOrdering', 285
  `IsBasis', 601
  `IsBasisByNiceBasis', 612
  `IsBasisOfAlgebraModuleElementSpace', 634
  `IsBergerCondition', 824
  `IsBijective', 306
  `IsBinaryRelation', 314
    \sub same as `IsEndoGeneralMapping', 314
  `IsBLetterAssocWordRep', 337
  `IsBLetterWordsFamily', 337
  `IsBlist', 210
  `IsBlockMatrixRep', 239
  `IsBool', 169
  `IsBound', for lists, 178
  IsBound and Unbind for Lists, \indexit{178}
  IsBound and Unbind for Records, \indexit{265}
  `IsBoundGlobal', 45
  `IsBrauerTable', 729
  `IsBravaisGroup', 433
  `IsBuiltFromAdditiveMagmaWithInverses', 346
  `IsBuiltFromGroup', 346
  `IsBuiltFromMagma', 346
  `IsBuiltFromMagmaWithInverses', 346
  `IsBuiltFromMagmaWithOne', 346
  `IsBuiltFromSemigroup', 346
  `IsCanonicalBasis', 604
  `IsCanonicalBasisFullMatrixModule', 608
  `IsCanonicalBasisFullRowModule', 608
  `IsCanonicalNiceMonomorphism', 389
  `IsCanonicalPcgs', 441
  `IsCentral', 323
  `IsCentralFactor', 382
  `IsChar', 249
  `IsCharacter', 776
  `IsCharacteristicSubgroup', 352
  `IsCharacterTable', 729
  `IsCharacterTableInProgress', 729
  `IsCharCollection', 249
  `IsCheapConwayPolynomial', 589
  `IsClassFunction', 767
  `IsClassFusionOfNormalSubgroup', 745
  `IsClosedStream', 97
  `IsCochain', 655
  `IsCochainCollection', 655
  `IsCollection', 267
  `IsCollectionFamily', 267
  `IsCommutative', 323
  `IsCommutativeElement', 301
  `IsCommutativeElementCollColl', 301
  `IsCommutativeElementCollection', 301
  `IsCompositionMappingRep', 304
  `IsConfluent', 344
    \sub for pc groups, 455
  `Is\-Conjugacy\-Class\-Subgroups\-By\-Stabilizer\-Rep', 373
  `IsConjugacyClassSubgroupsRep', 373
  `IsConjugate', 361
  `IsConjugatorAutomorphism', 390
  `IsConjugatorIsomorphism', 390
  `IsConstantRationalFunction', 673
  `IsConstantTimeAccessGeneralMapping', 312
  `IsConstantTimeAccessList', 173
  `IsContainedInSpan', 606
  `IsCopyable', 112
  `IsCyc', 158
  `IsCyclic', 366
    \sub for character tables, 735
  `IsCyclicTom', 711
  `IsCyclotomic', 158
  `IsCyclotomicField', 593
  `IsCyclotomicMatrixGroup', 432
  `IsDenseList', 172
  `IsDiagonalMat', 226
  `IsDigitChar', 253
  `IsDirectoryPath', 93
  `IsDistributive', 567
  `IsDivisionRing', 577
  `IsDomain', 291
  `IsDoneIterator', 278
  `IsDoubleCoset', 359
  `IsDuplicateFree', 194
  `IsDuplicateFreeList', 194
  `IsDxLargeGroup', 755
  `IsElementaryAbelian', 366
    \sub for character tables, 735
  `IsElementOfFpMonoid', 549
  `IsElementOfFpSemigroup', 549
  `IsElementOfFreeMagmaRing', 664
  `IsElementOfFreeMagmaRingCollection', 664
  `IsElementOfFreeMagmaRingFamily', 664
  `IsElementOfMagmaRingModuloRelations', 665
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Collection', 665
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Relations\-Family', 665
  `Is\-Element\-Of\-Magma\-Ring\-Modulo\-Span\-Of\-Zero\-Family', 666
  `IsEmpty', 272
  `IsEmptyString', 252
  `IsEndOfStream', 100
  `IsEndoGeneralMapping', 312
    \sub same as `IsBinaryRelation', 314
  `IsEqualSet', 196
  `IsEquivalenceClass', 318
  `IsEquivalenceRelation', 315
  `IsEuclideanRing', 569
  `IsEvenInt', 127
  `IsExecutableFile', 93
  `IsExistingFile', 93
  `IsExtAElement', 299
  `IsExternalOrbit', 409
  `IsExternalSet', 408
  `IsExternalSubset', 409
  `IsExtLElement', 299
  `IsExtRElement', 299
  `IsFamilyPcgs', 453
  `IsFFE', 583
  `IsFFECollColl', 583
  `IsFFECollection', 583
  `IsField', 577
  `IsFieldControlledByGaloisGroup', 580
  `IsFieldHomomorphism', 312
  `IsFinite', 272
    \sub for character tables, 735
  `IsFiniteDimensional', 575
    \sub for matrix algebras, 622
  `IsFiniteFieldPolynomialRing', 681
  `IsFinitelyGeneratedGroup', 367
  `IsFiniteOrderElement', 301
  `IsFiniteOrderElementCollColl', 301
  `IsFiniteOrderElementCollection', 301
  `IsFiniteOrdersPcgs', 437
  `IsFixedStabilizer', 426
  `IsFLMLOR', 621
  `IsFLMLORWithOne', 621
  `IsFpGroup', 463
  `IsFpMonoid', 549
  `IsFpSemigroup', 549
  `IsFreeGroup', 331
  `IsFreeLeftModule', 575
  `IsFreeMagmaRing', 663
  `IsFreeMagmaRingWithOne', 663
  `IsFromFpGroupGeneralMappingByImages', 395
  `IsFromFpGroupHomomorphismByImages', 395
  `Is\-From\-Fp\-Group\-Std\-Gens\-General\-Mapping\-By\-Images', 395
  `Is\-From\-Fp\-Group\-Std\-Gens\-Homomorphism\-By\-Images', 395
  `IsFullHomModule', 611
  `IsFullMatrixModule', 576
  `IsFullRowModule', 576
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Bilinear\-Form', 431
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Quadratic\-Form', 432
  `Is\-Full\-Subgroup\-GLor\-SLRespecting\-Sesquilinear\-Form', 431
  `IsFullTransformationSemigroup', 540
  `IsFunction', 63
  `IsGAPRandomSource', 136
  `IsGaussianIntegers', 597
  `IsGaussianRationals', 592
  `IsGaussianSpace', 606
  `IsGaussInt', 160
  `IsGaussRat', 160
  `IsGeneralizedDomain', 291
  `IsGeneralizedRowVector', 184
  `IsGeneralLinearGroup', 430
  `IsGeneralMapping', 312
  `IsGeneralMappingFamily', 313
  `IsGeneratorsOf<Struct>', 288
  `IsGL', 430
  `IsGlobalRandomSource', 136
  `IsGreensClass', 542
  `IsGreensDClass', 542
  `IsGreensDRelation', 542
  `IsGreensHClass', 542
  `IsGreensHRelation', 542
  `IsGreensJClass', 542
  `IsGreensJRelation', 542
  `IsGreensLClass', 542
  `IsGreensLessThanOrEqual', 542
  `IsGreensLRelation', 542
  `IsGreensRClass', 542
  `IsGreensRelation', 542
  `IsGreensRRelation', 542
  `IsGroup', 350
  `IsGroupGeneralMapping', 310
  `Is\-Group\-General\-Mapping\-By\-As\-Group\-General\-Mapping\-By\-Images', 395
  `IsGroupGeneralMappingByImages', 395
  `IsGroupGeneralMappingByPcgs', 395
  `IsGroupHClass', 543
  `IsGroupHomomorphism', 310
  `IsGroupOfAutomorphisms', 391
  `IsGroupRing', 663
  `IsHandledByNiceBasis', 576
    \sub for vector spaces, 612
  `IsHandledByNiceMonomorphism', 389
  `IsHasseDiagram', 315
  `IsHomogeneousList', 173
  `IsIdempotent', 294
  `IsIdenticalObj', 110
  `IsIncomparableUnder', 281
  `IsInducedFromNormalSubgroup', 826
  `IsInducedPcgs', 440
  `IsInducedPcgsWrtSpecialPcgs', 448
  `IsInfBitsFamily', 337
  `IsInfinity', 160
  `IsInjective', 306
  `IsInnerAutomorphism', 390
  `IsInputOutputStream', 104
  `IsInputStream', 97
  `IsInputTextNone', 97
  `IsInputTextStream', 97
  `IsInt', 127
  `IsIntegerMatrixGroup', 433
  `IsIntegers', 126
  `IsIntegralBasis', 604
  `IsIntegralCyclotomic', 158
  `IsIntegralRing', 566
  `IsInternallyConsistent', 114
    \sub for character tables, 744
    \sub for tables of marks, 712
  `IsIrreducibleCharacter', 776
  `IsIrreducibleRingElement', 568
  `IsIterator', 278
  `IsJacobianElement', 301
  `IsJacobianElementCollColl', 301
  `IsJacobianElementCollection', 301
  `IsJacobianRing', 567
  `IsLaurentPolynomial', 672
  `IsLaurentPolynomialDefaultRep', 688
  `IsLDistributive', 567
  `IsLeftAlgebraModuleElement', 633
  `IsLeftAlgebraModuleElementCollection', 633
  `IsLeftIdeal', 564
  `IsLeftIdealInParent', 564
  `IsLeftModule', 573
  `IsLeftModuleGeneralMapping', 311
  `IsLeftModuleHomomorphism', 311
  `IsLeftOperatorAdditiveGroup', 573
  `IsLeftSemigroupIdeal', 540
  `IsLeftVectorSpace', 598
  `IsLessThanOrEqualUnder', 281
  `IsLessThanUnder', 281
  `IsLetterAssocWordRep', 336
  `IsLetterWordsFamily', 336
  `IsLexicographicallyLess', 200
  `IsLexOrderedFFE', 584
  `IsLieAbelian', 644
  `IsLieAlgebra', 621
  `IsLieMatrix', 223
  `IsLieNilpotent', 644
  `IsLieObject', 639
  `IsLieObjectCollection', 639
  `IsLieSolvable', 644
  `IsLinearMapping', 311
  `IsLinearMappingsModule', 611
  `IsList', 172
  `IsListDefault', 185
  `IsListOrCollection', 268
  `IsLogOrderedFFE', 584
  `IsLowerAlphaChar', 253
  `IsLowerTriangularMat', 226
  `IsMagma', 319
  `IsMagmaHomomorphism', 309
  `IsMagmaRingModuloRelations', 665
  `IsMagmaRingModuloSpanOfZero', 666
  `IsMagmaWithInverses', 319
  `IsMagmaWithInversesIfNonzero', 319
  `IsMagmaWithOne', 319
  `IsMapping', 305
  `IsMatchingSublist', 193
  `IsMatrix', 222
  `IsMatrixGroup', 429
  `IsMatrixModule', 576
  `IsMatrixSpace', 606
  `IsMersenneTwister', 136
  `IsMinimalNonmonomial', 829
  `IsModuloPcgs', 442
  `IsMonoid', 545
  `IsMonomial', for characters, 826
    \sub for character tables, 735
    \sub for groups, 826
    \sub for positive integers, 827
  `IsMonomialGroup', 366
  `IsMonomialMatrix', 226
  `IsMonomialNumber', 827
  `IsMonomialOrdering', 682
  `IsMultiplicativeElement', 299
  `IsMultiplicativeElementWithInverse', 300
  `IsMultiplicativeElementWithOne', 300
  `IsMultiplicativeElementWithZero', 300
  `IsMultiplicativeGeneralizedRowVector', 184
  `IsMultiplicativeZero', 323
  `IsMutable', 112
  `IsMutableBasis', 605
  `IsNaturalAlternatingGroup', 416
  `IsNaturalGL', 431
  `IsNaturalGLnZ', 433
  `IsNaturalSL', 431
  `IsNaturalSLnZ', 433
  `IsNaturalSymmetricGroup', 416
  `IsNearAdditiveElement', 299
  `IsNearAdditiveElementWithInverse', 299
  `IsNearAdditiveElementWithZero', 299
  `IsNearAdditiveGroup', 557
  `IsNearAdditiveMagma', 557
  `IsNearAdditiveMagmaWithInverses', 557
  `IsNearAdditiveMagmaWithZero', 557
  `IsNearlyCharacterTable', 729
  `IsNearRingElement', 300
  `IsNearRingElementWithInverse', 300
  `IsNearRingElementWithOne', 300
  `IsNegRat', 146
  `IsNilpotent', for character tables, 735
    \sub for groups with pcgs, 450
  `IsNilpotentElement', 651
  `IsNilpotentGroup', 366
  `IsNilpotentTom', 711
  `IsNonassocWord', 326
  `IsNonassocWordCollection', 326
  `IsNonassocWordWithOne', 326
  `IsNonassocWordWithOneCollection', 326
  `IsNonnegativeIntegers', 126
  `IsNonSPGeneralMapping', 313
  `IsNonTrivial', 272
  `IsNormal', 351
  `IsNormalBasis', 604
  `IsNotIdenticalObj', 111
  `IsNumberField', 593
  `IsObject', 109
  `IsOddInt', 127
  isomorphic, pc group, 456, 457
  `IsomorphicSubgroups', 393
  `IsomorphismFpAlgebra', 630
  `IsomorphismFpGroup', 472
    \sub for subgroups of fp groups, 474
  `IsomorphismFpGroupByGenerators', 472
  `IsomorphismFpGroupByGeneratorsNC', 472
  `IsomorphismFpGroupByPcgs', 454
  `IsomorphismFpSemigroup', 550
  `IsomorphismGroups', 393
  `IsomorphismMatrixAlgebra', 630
  `IsomorphismPcGroup', 457
  `IsomorphismPermGroup', 416
    \sub for Imf matrix groups, 536
  `IsomorphismPermGroupImfGroup', 537
  `IsomorphismReesMatrixSemigroup', 544
  `IsomorphismRefinedPcGroup', 456
  `Isomorphism<Rep><Struct>', 289
  isomorphisms, find all, 393
  `IsomorphismSCAlgebra', 631
  `IsomorphismSimplifiedFpGroup', 475
  `IsomorphismSpecialPcGroup', 457
  `IsomorphismTransformationSemigroup', 540
  `IsomorphismTypeInfoFiniteSimpleGroup', 367
  `IsOne', 294
  `IsOperation', 63
  `IsOrdering', 280
  `IsOrderingOnFamilyOfAssocWords', 282
  `IsOrdinaryMatrix', 222
  `IsOrdinaryTable', 729
  `IsOutputStream', 97
  `IsOutputTextNone', 98
  `IsOutputTextStream', 98
  `IsPadicExtensionNumber', 695
  `IsPadicExtensionNumberFamily', 695
  `IsParentPcgsFamilyPcgs', 453
  `IsPartialOrderBinaryRelation', 315
  `IsPcGroup', 454
  `IsPcGroupGeneralMappingByImages', 395
  `IsPcGroupHomomorphismByImages', 395
  `IsPcgs', 436
  `IsPcgsCentralSeries', 444
  `IsPcgsChiefSeries', 445
  `IsPcgsElementaryAbelianSeries', 444
  `IsPcgsPCentralSeriesPGroup', 445
  `IsPerfect', for character tables, 735
  `IsPerfectGroup', 366
  `IsPerfectTom', 711
  `IsPerm', 411
  `IsPermCollColl', 411
  `IsPermCollection', 411
  `IsPermGroup', 415
  `IsPermGroupGeneralMappingByImages', 395
  `IsPermGroupHomomorphismByImages', 395
  `IsPGroup', 367
  `IsPNilpotent', 368
  `IsPolycyclicGroup', 366
  `IsPolynomial', 672
  `IsPolynomialDefaultRep', 688
  `IsPolynomialFunction', 671
  `IsPolynomialFunctionsFamily', 686
  `IsPolynomialRing', 681
  `IsPosInt', 127
  `IsPositiveIntegers', 126
  `IsPosRat', 146
  `Is\-Preimages\-By\-As\-Group\-General\-Mapping\-By\-Images', 395
  `IsPreOrderBinaryRelation', 315
  `IsPrime', 568
  `IsPrimeField', 579
  `IsPrimeInt', 131
  `IsPrimeOrdersPcgs', 437
  `IsPrimePowerInt', 132
  `IsPrimitive', 407
  `IsPrimitiveCharacter', 825
  `IsPrimitivePolynomial', 673
  `IsPrimitiveRootMod', 140
  `IsProbablyPrimeInt', 131
  `IsPseudoCanonicalBasisFullHomModule', 611
  `IsPSolvable', 368
  `IsPSolvableCharacterTable', 745
  `IsPSolvableCharacterTableOp', 745
  `IsPurePadicNumber', 694
  `IsPurePadicNumberFamily', 694
  `IsQuasiPrimitive', 825
  `IsQuaternion', 622
  `IsQuaternionCollColl', 622
  `IsQuaternionCollection', 622
  `IsQuickPositionList', 208
  `IsQuotientSemigroup', 541
  `IsRandomSource', 136
  `IsRange', 207
  `IsRat', 145
  `IsRationalFunction', 671
  `IsRationalFunctionDefaultRep', 688
  `IsRationalFunctionsFamily', 686
  `IsRationalMatrixGroup', 432
  `IsRationals', 145
  `IsRationalsPolynomialRing', 681
  `IsRDistributive', 567
  `IsReadableFile', 93
  `IsReadOnlyGlobal', 44
  `IsRecord', 261
  `IsRecordCollColl', 261
  `IsRecordCollection', 261
  `IsReduced', 345
  `IsReductionOrdering', 282
  `IsReesCongruence', 541
  `IsReesCongruenceSemigroup', 540
  `IsReesMatrixSemigroup', 543
  `IsReesMatrixSemigroupElement', 544
  `IsReesZeroMatrixSemigroup', 543
  `IsReesZeroMatrixSemigroupElement', 544
  `IsReflexiveBinaryRelation', 314
  `IsRegular', 406
  `IsRegularDClass', 543
  `IsRegularSemigroup', 539
  `IsRegularSemigroupElement', 539
  `IsRelativelySM', 828
  `IsRestrictedLieAlgebra', 649
  `IsRewritingSystem', 344
  `IsRightAlgebraModuleElement', 633
  `IsRightAlgebraModuleElementCollection', 633
  `IsRightCoset', 357
  `IsRightIdeal', 564
  `IsRightIdealInParent', 564
  `IsRightModule', 574
  `IsRightOperatorAdditiveGroup', 573
  `IsRightSemigroupIdeal', 540
  `IsRing', 561
  `IsRingElement', 300
  `IsRingElementWithInverse', 300
  `IsRingElementWithOne', 300
  `IsRingGeneralMapping', 312
  `IsRingHomomorphism', 312
  `IsRingWithOne', 565
  `IsRingWithOneGeneralMapping', 312
  `IsRingWithOneHomomorphism', 312
  `IsRootSystem', 646
  `IsRootSystemFromLieAlgebra', 646
  `IsRowModule', 576
  `IsRowSpace', 606
  `IsRowVector', 214
  `IsScalar', 300
  `IsSemiEchelonized', 607
  `IsSemigroup', 538
  `IsSemigroupCongruence', 541
  `IsSemigroupIdeal', 540
  `IsSemiRegular', 406
  `IsSet', 194
  `IsShortLexLessThanOrEqual', 333
  `IsShortLexOrdering', 283
  `IsSimple', for character tables, 735
  `IsSimpleAlgebra', 622
  `IsSimpleGroup', 366
  `IsSimpleSemigroup', 539
  `IsSingleValued', 305
  `IsSL', 431
  `IsSolvable', for character tables, 735
  `IsSolvableGroup', 366
  `IsSolvableTom', 711
  `IsSortedList', 194
  `IsSpecialLinearGroup', 431
  `IsSpecialPcgs', 447
  `IsSPGeneralMapping', 313
  `IsSporadicSimple', for character tables, 735
  `IsSSortedList', 194
  `IsStandardGeneratorsOfGroup', 717
  `IsStraightLineProgElm', 342
  `IsStraightLineProgram', 338
  `IsStream', 97
  `IsString', 249
  `IsStringRep', 252
  `Is<Struct>', 289
  `IsSubgroup', 351
  `IsSubgroupFpGroup', 463
  `IsSubgroupOfWholeGroupByQuotientRep', 476
  `IsSubgroupSL', 431
  `IsSubmonoidFpMonoid', 548
  `IsSubnormal', 352
  `IsSubnormallyMonomial', 828
  `IsSubsemigroupFpSemigroup', 548
  `IsSubset', 274
  `IsSubsetBlist', 211
  `IsSubsetLocallyFiniteGroup', 367
  `IsSubsetSet', 197
  `IsSubspacesVectorSpace', 600
  `IsSub<struct>', 291
  `IsSupersolvable', for character tables, 735
    \sub for groups with pcgs, 450
  `IsSupersolvableGroup', 366
  `IsSurjective', 306
  `IsSyllableAssocWordRep', 337
  `IsSyllableWordsFamily', 337
  `IsSymmetricBinaryRelation', 315
  `IsSymmetricGroup', 417
  `IsTable', 173
  `IsTableOfMarks', 707
  `IsTableOfMarksWithGens', 718
  `IsToPcGroupGeneralMappingByImages', 395
  `IsToPcGroupHomomorphismByImages', 395
  `IsToPermGroupGeneralMappingByImages', 395
  `IsToPermGroupHomomorphismByImages', 395
  `IsTotal', 305
  `IsTotalOrdering', 281
  `IsTransformation', 554
  `IsTransformationCollection', 554
  `IsTransformationMonoid', 540
  `IsTransformationSemigroup', 540
  `IsTransitive', for characters, 779
    \sub for class functions, 779
    \sub for group actions, 406
  `IsTransitiveBinaryRelation', 315
  `IsTranslationInvariantOrdering', 282
  `IsTrivial', 272
  `IsTuple', 303
  `IsTwoSidedIdeal', 564
  `IsTwoSidedIdealInParent', 564
  `IsUEALatticeElement', 658
  `IsUEALatticeElementCollection', 658
  `IsUEALatticeElementFamily', 658
  `IsUniqueFactorizationRing', 566
  `IsUnit', 567
  `IsUnivariatePolynomial', 672
  `IsUnivariatePolynomialRing', 682
  `IsUnivariateRationalFunction', 672
  `IsUnknown', 167
  `IsUpperAlphaChar', 253
  `IsUpperTriangularMat', 226
  `IsValidIdentifier', 42
  `IsVector', 300
  `IsVectorSpace', 598
  `IsVirtualCharacter', 776
  `IsWeightLexOrdering', 284
  `IsWeightRepElement', 659
  `IsWeightRepElementCollection', 659
  `IsWeightRepElementFamily', 659
  `IsWellFoundedOrdering', 281
  `IsWeylGroup', 647
  `IsWholeFamily', 273
  `IsWLetterAssocWordRep', 337
  `IsWLetterWordsFamily', 337
  `IsWord', 325
  `IsWordCollection', 326
  `IsWordWithInverse', 325
  `IsWordWithOne', 325
  `IsWreathProductOrdering', 285
  `IsWritableFile', 93
  `IsZero', 294
  `IsZeroGroup', 540
  `IsZeroSimpleSemigroup', 539
  `IsZeroSquaredElement', 302
  `IsZeroSquaredElementCollColl', 302
  `IsZeroSquaredElementCollection', 302
  `IsZeroSquaredRing', 567
  `IsZmodnZObj', 135
  `IsZmodnZObjNonprime', 135
  `IsZmodpZObj', 135
  `IsZmodpZObjLarge', 135
  `IsZmodpZObjSmall', 135
  `Iterated', 205
  `Iterator', 277
  iterator, for low index subgroups, 471
  `IteratorByBasis', 603
  `IteratorByFunctions', 279
  `IteratorList', 279
  Iterators, \indexit{277}
  `IteratorSorted', 278
\letter J
  $j_N$, 162
  `Jacobi', 140
  `JenningsLieAlgebra', 650
  `JenningsSeries', 371
  `JoinEquivalenceRelations', 317
  `JoinStringsWithSeparator', 256
  `JordanDecomposition', 235
\letter K
  $k_N$, 162
  `KappaPerp', 651
  `KB_REW', 552
  `KernelOfAdditiveGeneralMapping', 311
  `KernelOfCharacter', 778
  `KernelOfMultiplicativeGeneralMapping', 310
  `KernelOfTransformation', 555
  Keywords, \indexit{41}
  `KillingMatrix', 651
  `KnownAttributesOfObject', 121
  Known Problems of the Configure Process, \indexit{837}
  `KnownPropertiesOfObject', 124
  `KnownTruePropertiesOfObject', 124
  `KnowsHowToDecompose', 383
  `KnuthBendixRewritingSystem', 553
  Krasner-Kaloujnine theorem, 508
  `KroneckerProduct', 228
  `KuKGenerators', 508
\letter L
  $l_N$, 162
  `Lambda', 138
  Language Overview, \indexit{39}
  larger or equal, 47
  larger test, 47
  `LargestElementGroup', 379
  `LargestElementStabChain', 424
  `LargestMovedPoint', 412
  `LargestUnknown', 167
  `last', 64
  `LastSystemError', 90
  `LaTeXStringDecompositionMatrix', 743
  lattice base reduction, 245, 246
  lattice basis reduction, for virtual characters, 783
  `LatticeByCyclicExtension', 376
  `LatticeGeneratorsInUEA', 658
  Lattice Reduction, \indexit{245}
  `LatticeSubgroups', 374
  `LatticeSubgroupsByTom', 705
  `LaurentPolynomialByCoefficients', 679
  `LaurentPolynomialByExtRep', 689
  `LaurentPolynomialByExtRepNC', 689
  Laurent Polynomials, \indexit{679}
  `LClassOfHClass', 542
  `Lcm', 571
  `LcmInt', 130
  `LcmOp', 571
  `LeadCoeffsIGS', 441
  `LeadingCoefficient', 674
  `LeadingCoefficientOfPolynomial', 683
  `LeadingExponentOfPcElement', 438
  `LeadingMonomial', 675
  `LeadingMonomialOfPolynomial', 682
  `LeadingTermOfPolynomial', 682
  Leaving GAP, \indexit{73}
  `LeftActingAlgebra', 634
  `LeftActingDomain', 574
  `LeftActingRingOfIdeal', 565
  `LeftAlgebraModule', 632
  `LeftAlgebraModuleByGenerators', 632
  left cosets, 357
  `LeftDerivations', 641
  `LeftIdeal', 563
  `LeftIdealByGenerators', 564
  `LeftIdealNC', 564
  `LeftModuleByGenerators', 574
  `LeftModuleByHomomorphismToMatAlg', 635
  `LeftModuleGeneralMappingByImages', 609
  `LeftModuleHomomorphismByImages', 609
  `LeftModuleHomomorphismByImagesNC', 609
  `LeftModuleHomomorphismByMatrix', 610
  `LeftQuotient', 296
    \sub for words, 334
  `LeftShiftRowVector', 218
  legacy, 849
  `Legendre', 141
  `Length', 194
    \sub of an associative word, 334
  length, of a word, 334
  `LengthsTom', 708
  `LenstraBase', 595
  `LessThanFunction', 281
  `LessThanOrEqualFunction', 281
  `LetterRepAssocWord', 337
  `LevelsOfGenerators', 285
  `LeviMalcevDecomposition', 627
    \sub for Lie algebras, 645
  Lexical Structure, \indexit{40}
  `LexicographicOrdering', 282
  `LGFirst', 448
  `LGLayers', 448
  `LGLength', 448
  `LGWeights', 447
  library tables, 726
  `LieAlgebra', 640
  `LieAlgebraByStructureConstants', 640
  `LieBracket', 296
  `LieCenter', 642
  `LieCentralizer', 642
  `LieCentre', 642
  `LieCoboundaryOperator', 655
  `LieDerivedSeries', 643
  `LieDerivedSubalgebra', 643
  `LieFamily', 640
  `LieLowerCentralSeries', 644
  `LieNilRadical', 643
  `LieNormalizer', 642
  `LieObject', 639
  Lie objects, \indexit{639}
  `LieSolvableRadical', 643
  `LieUpperCentralSeries', 644
  `LiftedInducedPcgs', 443
  `LiftedPcElement', 443
  `LinearAction', 449
  `LinearActionLayer', 449
  `LinearCharacters', 735
  `LinearCombination', 603
  `LinearCombinationPcgs', 438
  Linear equations over the integers and Integral Matrices, \indexit{240}
  `LinearIndependentColumns', 245
  Linear Mappings, \indexit{311}
  `LinearOperation', 449
  `LinearOperationLayer', 449
  Line Editing, \indexit{74}
  `LinesOfStraightLineProgram', 339
  `List', 202
  list and non-list, difference, 187
    \sub left quotient, 189
    \sub mod, 189
    \sub product, 188
    \sub quotient, 189
  List Assignment, \indexit{176}
  list assignment, operation, 174
  `ListBlist', 211
  list boundedness test, operation, 174
  List Categories, \indexit{172}
  list element, access, 174
    \sub assignment, 176
    \sub operation, 174
  List Elements, \indexit{174}
  list equal, comparison, 183
  `ListN', 205
  list of available books, 23
  `ListPerm', 414
  Lists and Collections, \indexit{268}
  list smaller, comparison, 183
  `ListStabChain', 424
  list unbind, operation, 174
  `ListWithIdenticalEntries', 190
  `ListX', 205
  `LLL', 783
  LLL algorithm, for Gram matrices, 246
    \sub for vectors, 245
    \sub for virtual characters, 783
  `LLLReducedBasis', 245
  `LLLReducedGramMat', 246
  `LoadDynamicModule', 35
  Loading a GAP Package, \indexit{845}
  loading a saved workspace, 37
  `LoadPackage', 845
  `local', 55
  logarithm, discrete, 140
    \sub of a root of unity, 160
  `LogFFE', 585
  logical, 169
  logical operations, 170
  `LogInt', 128
  `LogMod', 139
  `LogModShanks', 139
  `LogTo', 95
    \sub for streams, 101
    \sub stop logging, 95
  `LongestWeylWordPerm', 648
  loop, read eval print, 64
  loop, `for', 53
    \sub `repeat', 52
    \sub `while', 52
  loop over iterator, 54
  loop over object, 54
  loop over range, 53
  loops, leaving, 55
    \sub restarting, 55
  `LowercaseString', 254
  `LowerCentralSeriesOfGroup', 370
  Low Index Subgroups, \indexit{471}
  `LowIndexSubgroupsFpGroup', 471
  `LowIndexSubgroupsFpGroupIterator', 471
  Low Level Routines to Modify and Create Stabilizer Chains, \indexit{425}
  `Lucas', 155
\letter M
  $m_N$, 162
  Macintosh, 840, 841
  MacOS, 841
  `Magma', 320
  `MagmaByGenerators', 320
  `MagmaByMultiplicationTable', 321
  Magma Categories, \indexit{319}
  `MagmaElement', 321
  Magma Generation, \indexit{320}
  `MagmaHomomorphismByFunctionNC', 309
  Magma Homomorphisms, \indexit{309}
  `MagmaRingModuloSpanOfZero', 666
  Magma Rings modulo Relations, \indexit{665}
  Magma Rings modulo the Span of a Zero Element, \indexit{666}
  Magmas Defined by Multiplication Tables, \indexit{321}
  `MagmaWithInverses', 320
  `MagmaWithInversesByGenerators', 320
  `MagmaWithInversesByMultiplicationTable', 321
  `MagmaWithOne', 320
  `MagmaWithOneByGenerators', 320
  `MagmaWithOneByMultiplicationTable', 321
  Main Loop, \indexit{64}
  `MakeConfluent', 345
  `MakeImmutable', 112
  `MakeReadOnlyGlobal', 44
  `MakeReadWriteGlobal', 44
  Making transformation semigroups, \indexit{540}
  Manual Conventions, \indexit{20}
  map, parametrized, 810
  `MappedWord', 327
  `MappingByFunction', 304
  `MappingPermListList', 414
  Mappings that Respect Addition, \indexit{311}
  Mappings that Respect Multiplication, \indexit{310}
  Mappings which are Compatible with Algebraic Structures, \indexit{309}
  maps, 801
  `MarksTom', 708
  `MatAlgebra', 618
  `MatClassMultCoeffsCharTable', 747
  `MathieuGroup', 512
  `MatLieAlgebra', 641
  matrices, commutator, 225
  Matrices as Basis of a Row Space, \indexit{233}
  Matrices as Linear Mappings, \indexit{234}
  Matrices over Finite Fields, \indexit{236}
  Matrices Representing Linear Equations and the Gaussian Algorithm, \indexit{229}
  `MatrixAlgebra', 618
  `MatrixAutomorphisms', 762
  matrix automorphisms, 804
  `MatrixByBlockMatrix', 239
  Matrix Constructions, \indexit{227}
  Matrix Groups in Characteristic 0, \indexit{432}
  `MatrixLieAlgebra', 641
  `MatrixOfAction', 634
  matrix spaces, 606
  `MatScalarProducts', 777
  `MatTom', 710
  `MaximalAbelianQuotient', 372
  `MaximalBlocks', 407
  `MaximalNormalSubgroups', 374
  `MaximalSubgroupClassReps', 373
  `MaximalSubgroups', 373
    \sub for groups with pcgs, 450
  `MaximalSubgroupsLattice', 375
  `MaximalSubgroupsTom', 714
  `Maximum', 200
  `MaximumList', 201
  MeatAxe Modules, \indexit{696}
  `MeetEquivalenceRelations', 317
  `MeetMaps', 813
  Membership Test for Collections, \indexit{276}
  Membership Test for Lists, \indexit{182}
  `MemoryUsage', 114
  `MinimalElementCosetStabChain', 424
  `MinimalGeneratingSet', 379
    \sub for groups with pcgs, 450
  `MinimalNonmonomialGroup', 829
  Minimal Nonmonomial Groups, \indexit{829}
  `MinimalNormalSubgroups', 374
  `MinimalPolynomial', 676
    \sub over a field, 580
    \sub over a ring, 676
  Minimal Polynomials, \indexit{676}
  `MinimalStabChain', 422
  `MinimalSupergroupsLattice', 375
  `MinimalSupergroupsTom', 715
  `MinimizedBombieriNorm', 678
  `Minimum', 200
  `MinimumList', 201
  `MinusCharacter', 819
  Miscellaneous, \indexit{144}
  Miscellaneous Name Changes or Removed Names, \indexit{850}
  mod, integers, 135
    \sub laurent polynomials, 670
    \sub lists, 189
    \sub rationals, 48
  `mod', 48
    \sub arithmetic operators, 48
    \sub for character tables, 733
    \sub residue class rings, 134
  modular inverse, 48
  modular remainder, 48
  modular roots, 142
  `ModuleByRestriction', 636
  Module Constructions, \indexit{696}
  Module Homomorphisms, \indexit{699}
  `ModuleOfExtension', 459
  Modules over Lie Algebras and Their Cohomology, \indexit{654}
  Modules over Semisimple Lie Algebras, \indexit{656}
  modulo, 48
    \sub arithmetic operators, 48
    \sub for pcgs, 442
    \sub residue class rings, 134
  `ModuloPcgs', 442
  `MoebiusMu', 143
  `MoebiusTom', 710
  Molien Series, \indexit{790}
  `MolienSeries', 790
  `MolienSeriesInfo', 791
  `MolienSeriesWithGivenDenominator', 792
  `Monoid', 545
  `MonoidByGenerators', 545
  `MonoidByMultiplicationTable', 546
  `MonoidOfRewritingSystem', 553
  `MonomialComparisonFunction', 683
  `MonomialExtGrlexLess', 685
  `MonomialExtrepComparisonFun', 683
  `MonomialGrevlexOrdering', 684
  `MonomialGrlexOrdering', 684
  `MonomialLexOrdering', 683
  Monomial Orderings, \indexit{682}
  `MonomialTotalDegreeLess', 850
  monomorphisms, find all, 393
  `MorClassLoop', 393
  More about Boolean Lists, \indexit{213}
  More About Global Variables, \indexit{44}
  More about Tables of Marks, \indexit{702}
  `MostFrequentGeneratorFpGroup', 469
  `MovedPoints', 413
  Moved Points of Permutations, \indexit{412}
  `MTX.BasesCompositionSeries', 698
  `MTX.BasesMaximalSubmodules', 698
  `MTX.BasesMinimalSubmodules', 697
  `MTX.BasesMinimalSupermodules', 698
  `MTX.BasesSubmodules', 697
  `MTX.BasisInOrbit', 699
  `MTX.BasisRadical', 698
  `MTX.BasisSocle', 698
  `MTX.CollectedFactors', 698
  `MTX.CompositionFactors', 698
  `MTX.DegreeSplittingField', 697
  `MTX.Dimension', 697
  `MTX.Distinguish', 699
  `MTX.Field', 697
  `MTX.Generators', 697
  `MTX.Homomorphism', 699
  `MTX.Homomorphisms', 699
  `MTX.InducedAction', 698
  `MTX.InducedActionFactorMatrix', 698
  `MTX.InducedActionFactorModule', 698
  `MTX.InducedActionMatrix', 698
  `MTX.InducedActionMatrixNB', 698
  `MTX.InducedActionSubmodule', 698
  `MTX.InducedActionSubmoduleNB', 698
  `MTX.InvariantBilinearForm', 699
  `MTX.InvariantQuadraticForm', 699
  `MTX.InvariantSesquilinearForm', 699
  `MTX.IsAbsolutelyIrreducible', 697
  `MTX.IsEquivalent', 699
  `MTX.IsIrreducible', 697
  `MTX.Isomorphism', 699
  `MTX.NormedBasisAndBaseChange', 698
  `MTX.OrthogonalSign', 699
  `MTX.ProperSubmoduleBasis', 697
  `MTX.SubGModule', 697
  `MTX.SubmoduleGModule', 697
  multiplication, 48
    \sub matrices, 224
    \sub matrix and matrix list, 225
    \sub matrix and scalar, 223
    \sub matrix and vector, 224
    \sub operation, 296
    \sub scalar and matrix, 223
    \sub scalar and matrix list, 225
    \sub scalar and vector, 215
    \sub vector and matrix, 224
    \sub vector and matrix list, 225
    \sub vector and scalar, 215
    \sub vectors, 215
  `MultiplicationTable', 321
  Multiplicative Arithmetic for Lists, \indexit{187}
  Multiplicative Arithmetic Functions, \indexit{142}
  `MultiplicativeNeutralElement', 323
  multiplicative order of an integer, 139
  `MultiplicativeZero', 323
  `MultiplicativeZeroOp', 293
  multiplicity, of constituents of a group character, 777
  multiplier, 382
  multisets, 196
  Multivariate Polynomials, \indexit{676}
  `MultRowVector', 218
  Murnaghan components, 789, 790
  Mutability and Copyability, \indexit{111}
  Mutability Status and List Arithmetic, \indexit{189}
  Mutable Bases, \indexit{605}
  `MutableBasis', 605
  `MutableBasisOfClosureUnderAction', 624
  `Mutable\-Basis\-Of\-Ideal\-In\-Nonassociative\-Algebra', 625
  `MutableBasisOfNonassociativeAlgebra', 625
  `MutableCopyMat', 228
  `MutableIdentityMat', 228
  `MutableNullMat', 228
\letter N
  $n_k$, 163
  `Name', 114
  `NameFunction', 61
  `NameRNam', 266
  `NamesFilter', 118
  `NamesGVars', 45
  `NamesLocalVariablesFunction', 61
  `NamesOfFusionSources', 808
  `NamesSystemGVars', 45
  `NamesUserGVars', 45
  `NaturalCharacter', 775
  Natural Embeddings related to Magma Rings, \indexit{664}
  `NaturalHomomorphismByGenerators', 309
  `NaturalHomomorphismByIdeal', 630
  `NaturalHomomorphismByNormalSubgroup', 372
  `NaturalHomomorphismByNormalSubgroupNC', 372
  `NaturalHomomorphismBySubAlgebraModule', 637
  `NaturalHomomorphismBySubspace', 610
  `NearAdditiveGroup', 558
  `NearAdditiveGroupByGenerators', 558
  `NearAdditiveMagma', 558
  `NearAdditiveMagmaByGenerators', 558
  `NearAdditiveMagmaWithZero', 558
  `NearAdditiveMagmaWithZeroByGenerators', 558
  `NearlyCharacterTablesFamily', 730
  negative number, 48
  `NegativeRoots', 646
  `NegativeRootVectors', 646
  `NestingDepthA', 185
  `NestingDepthM', 185
  `NewInfoClass', 80
  newline, 41
  newline character, 251
  `NewmanInfinityCriterion', 479
  New Presentations and Presentations for Subgroups, \indexit{474}
  `NextIterator', 278
  `NextPrimeInt', 132
  `NF', 592
  `NiceBasis', 612
  `NiceBasisFiltersInfo', 613
  `NiceFreeLeftModule', 612
  `NiceFreeLeftModuleInfo', 612
  `NiceMonomorphism', 389
  `NiceMonomorphismAutomGroup', 392
  Nice Monomorphisms, \indexit{389}
  `NiceObject', 389
  `NiceVector', 612
  `NilpotencyClassOfGroup', 366
  `NilpotentQuotientOfFpLieAlgebra', 653
  `NK', 163
  `NOAUTO', 846
  `NonabelianExteriorSquare', 382
  `NonnegativeIntegers', 126
  `NonnegIntScalarProducts', 815, 816
  `NonNilpotentElement', 651
  `Norm', 580
    \sub of character, 777
  `NormalBase', 582
  `NormalClosure', 362
  `NormalFormIntMat', 243
  Normal Forms of Integer Matrices - Name Changes, \indexit{850}
  Normal Forms over the Integers, \indexit{241}
  `NormalIntersection', 362
  `Normalized\-Element\-Of\-Magma\-Ring\-Modulo\-Relations', 665
  `NormalizedWhitespace', 255
  `Normalizer', 361
  normalizer, 361
  `NormalizerInGLnZ', 433
  `NormalizerInGLnZBravaisGroup', 433
  `NormalizersTom', 712
  `NormalizerTom', 712
  `NormalizeWhitespace', 255
  `NormalSeriesByPcgs', 446
  Normal Structure, \indexit{361}
  `NormalSubgroupClasses', 765
  `NormalSubgroupClassesInfo', 764
  `NormalSubgroups', 374
  `NormedRowVector', 216
  `NormedRowVectors', 609
  `NormedVectors', 850
  `not', 171
  `NrArrangements', 150
  `NrBasisVectors', 605
  `NrCombinations', 149
  `NrConjugacyClasses', 360
    \sub for character tables, 735
  `NrConjugacyClassesGL', 516
  `NrConjugacyClassesGU', 516
  `NrConjugacyClassesPGL', 516
  `NrConjugacyClassesPGU', 516
  `NrConjugacyClassesPSL', 516
  `NrConjugacyClassesPSU', 516
  `NrConjugacyClassesSL', 516
  `NrConjugacyClassesSLIsogeneous', 516
  `NrConjugacyClassesSU', 516
  `NrConjugacyClassesSUIsogeneous', 516
  `NrDerangements', 152
  `NrInputsOfStraightLineProgram', 339
  `NrMovedPoints', 413
  `NrOrderedPartitions', 154
  `NrPartitions', 153
  `NrPartitionsSet', 152
  `NrPartitionTuples', 155
  `NrPermutationsList', 151
  `NrPolyhedralSubgroups', 746
  `NrPrimitiveGroups', 527
  `NrRestrictedPartitions', 154
  `NrSubsTom', 708
  `NrTransitiveGroups', 518
  `NrTuples', 151
  `NrUnorderedTuples', 150
  `NullAlgebra', 619
  `NullMat', 227
  `NullspaceIntMat', 240
  `NullspaceMat', 229
  `NullspaceMatDestructive', 229
  `NullspaceModQ', 238
  `Number', 202
  number, Bell, 148
    \sub binomial, 147
    \sub Stirling, of the first kind, 148
    \sub Stirling, of the second kind, 149
  `NumberArgumentsFunction', 61
  `NumberFFVector', 217
  number field, 593
  number fields, Galois group, 596
  `NumberIrreducibleSolvableGroups', 529
  `NumberPerfectGroups', 523
  `NumberPerfectLibraryGroups', 523
  `NumberSmallGroups', 520
  `NumberSyllables', 335
  numerator, of a rational, 146
  `NumeratorOfModuloPcgs', 442
  `NumeratorOfRationalFunction', 671
  `NumeratorRat', 146
  Numerical Group Attributes, \indexit{368}
\letter O
  $O_p(G)$, see `PCore', 361
  `ObjByExtRep', 658
  Objects, \indexit{109}
  obsolete, 849
  `OCOneCocycles', 381
  octal character codes, 251
  `OctaveAlgebra', 618
  `od', 53
  `OldGeneratorsOfPresentation', 497
  `Omega', 365
  `ONanScottType', 417
  `OnBreak', 68
  `OnBreakMessage', 70
  `One', 292
  `OneAttr', 292
  `OneCoboundaries', 380
  `OneCocycles', 380
  one cohomology, 379
  `OneFactorBound', 678
  `OneImmutable', 292
  `OneIrreducibleSolvableGroup', 529
  `One<Library>Group', 518
  `OneMutable', 292
  `OneOfPcgs', 437
  `OneOp', 292
  `OnePrimitiveGroup', 518
  `OneSameMutability', 292
  `OneSM', 292
  `OneSmallGroup', 520
  `OneTransitiveGroup', 518
  `OnIndeterminates', 676
    \sub as a permutation action, 398
  `OnLeftInverse', 397
  `OnLines', 398
    \sub example, 513
  `OnPairs', 397
  `OnPoints', 397
  `OnRight', 397
  `OnSets', 397
  `OnSetsDisjointSets', 398
  `OnSetsSets', 397
  `OnSetsTuples', 398
  `OnSubspacesByCanonicalBasis', 399
  `OnTuples', 397
  `OnTuplesSets', 398
  `OnTuplesTuples', 398
  `Operation', 849
  `OperationAlgebraHomomorphism', 630
  Operational Structure of Domains, \indexit{286}
  `OperationHomomorphism', 849
  operations, for booleans, 170
  Operations and Attributes for Vector Spaces, \indexit{599}
  Operations applicable to All Streams, \indexit{98}
  Operations Concerning Blocks, \indexit{741}
  Operations for (Near-)Additive Magmas, \indexit{560}
  Operations for Abelian Number Fields, \indexit{592}
  operations for algebraic elements, 691
  Operations for Associative Words, \indexit{334}
  Operations for Associative Words by their Syllables, \indexit{335}
  Operations for Booleans, \indexit{170}
  Operations for Brauer Characters, \indexit{799}
  Operations for Class Functions, \indexit{776}
  Operations for Collections, \indexit{274}
  Operations for Cyclotomics, \indexit{157}
  Operations for Domains, \indexit{291}
  Operations for Finite Field Elements, \indexit{585}
  Operations for Finitely Presented Groups, \indexit{465}
  Operations for Group Homomorphisms, \indexit{386}
  Operations for Input Streams, \indexit{98}
  Operations for Lists, \indexit{198}
  Operations for Output Streams, \indexit{101}
  Operations for Pc Groups, \indexit{457}
  Operations for Rational Functions, \indexit{670}
  Operations for Special Kinds of Bases, \indexit{604}
  Operations for Stabilizer Chains, \indexit{423}
  Operations for Vector Space Bases, \indexit{602}
  Operations for Words, \indexit{327}
  Operations on elements of the algebra, \indexit{345}
  Operations on rewriting systems, \indexit{344}
  Operations to Evaluate Strings, \indexit{257}
  Operations to Produce or Manipulate Strings, \indexit{254}
  Operations which have Special Methods for Groups with Pcgs, \indexit{450}
  operators, 42
    \sub arithmetic, 48
    \sub associativity, 49
    \sub for cyclotomics, 161
    \sub for lists, 184
    \sub precedence, 48, 49
  Operators for Character Tables, \indexit{733}
  Operators for Matrices, \indexit{223}
  Operators for Row Vectors, \indexit{214}
  Optimization and Compiler Options, \indexit{838}
  options, 27, 830
    \sub command line, filenames, 29
    \sub command line, internal, 31
  options, under UNIX, 27
  `or', 170
  `Orbit', 399
  `OrbitFusions', 809
  `OrbitLength', 400
  `OrbitLengths', 400
  `OrbitLengthsDomain', 400
  `OrbitPerms', 415
  `OrbitPowerMaps', 804
  `Orbits', operation/attribute, 400
  Orbits, \indexit{399}
  `OrbitsDomain', 400
  `OrbitsPerms', 415
  `OrbitStabChain', 424
  `OrbitStabilizer', 401
  `OrbitStabilizerAlgorithm', 401
  Orbit Stabilizer Methods for Polycyclic Groups, \indexit{450}
  `Order', 295
    \sub of a class function, 773
  order,  of a group, 349
    \sub of a list, collection or domain, 273
    \sub of the prime residue group, 138
  `OrderedPartitions', 153
  ordering, booleans, 170
    \sub of records, 265
  `OrderingByLessThanFunctionNC', 280
  `OrderingByLessThanOrEqualFunctionNC', 280
  `OrderingOfRewritingSystem', 344
  `OrderingOnGenerators', 282
  `OrderingsFamily', 280
  Orderings on families of associative words, \indexit{282}
  `OrderMod', 139
  `OrderOfRewritingSystem', 344
  `OrdersClassRepresentatives', 736
  `OrdersTom', 708
  `Ordinal', 258
  ordinary character, 776
  `OrdinaryCharacterTable', 735
  `OrthogonalComponents', 789
  Orthogonal Embeddings, \indexit{247}
  `OrthogonalEmbeddings', 247
  `OrthogonalEmbeddingsSpecialDimension', 785
  OSX, 840
  Other Filters, \indexit{125}
  Other Operations Applicable to any Object, \indexit{114}
  Other Operations for Character Tables, \indexit{744}
  Other Operations for Tables of Marks, \indexit{712}
  output, suppressing, 64
  `OutputLogTo', 95
    \sub for streams, 102
    \sub stop logging output, 95
  `OutputTextFile', 103
  `OutputTextNone', 106
  `OutputTextString', 104
  `OutputTextUser', 104
\letter P
  $p$-group, 367
  package, 845
  Package Interface - Obsolete Functions and Name Changes, \indexit{849}
  Packages, \indexit{834}
  `PadicCoefficients', 245
  `PadicExtensionNumberFamily', 694
  `PadicNumber', 694
    \sub for pure padics, 693
  `PadicValuation', 569
  `Pager', 25
  `Parametrized', 812
  Parametrized Maps, \indexit{810}
  parametrized maps, 801
  `Parent', 290
  `ParentPcgs', 440
  Parents, \indexit{290}
  `PartialFactorization', 133
  partial order, 315
  `PartialOrderByOrderingFunction', 316
  `PartialOrderOfHasseDiagram', 315
  `Partitions', 153
  partitions, improper, of an integer, 154
    \sub ordered, of an integer, 154
    \sub restricted, of an integer, 154
  `PartitionsGreatestEQ', 154
  `PartitionsGreatestLE', 154
  `PartitionsSet', 152
  `PartitionTuples', 155
  `PcElementByExponents', 438
  `PcElementByExponentsNC', 438
  `PCentralLieAlgebra', 650
  `PCentralNormalSeriesByPcgsPGroup', 445
  `PCentralSeries', 371
  `PcGroupCode', 461
  `PcGroupCodeRec', 461
  `PcGroupFpGroup', 454
  Pc groups versus fp groups, \indexit{454}
  `PcGroupWithPcgs', 456
  `Pcgs', 436
  `Pcgs_OrbitStabilizer', 450
  Pcgs and Normal Series, \indexit{444}
  `PcgsByPcSequence', 436
  `PcgsByPcSequenceNC', 436
  `PcgsCentralSeries', 444
  `PcgsChiefSeries', 445
  `PcgsElementaryAbelianSeries', 444
  `PcgsPCentralSeriesPGroup', 445
  `PClassPGroup', 368
  `PCore', 361
  `PcSeries', 437
  `PerfectGroup', 522
  perfect groups, 522
  `PerfectIdentification', 523
  `PerfectResiduum', 363
  `Perform', 200
  `Permanent', 156
  Permanent of a Matrix, \indexit{156}
  `PermBounds', 798
  `PermCharInfo', 793
  `PermCharInfoRelative', 794
  `PermChars', 795
  `PermCharsTom', 721
  `PermComb', 798
  `PermLeftQuoTransformation', 556
  `PermList', 414
  `PermListList', 200
  `Permutation', 405
  `PermutationCharacter', 776
  permutation character, 821
  permutation characters, possible, 792, 795
  `PermutationCycle', 405
  `PermutationCycleOp', 405
  `PermutationGModule', 696
  `PermutationMat', 227
  `PermutationsFamily', 411
  Permutations Induced by Elements and Cycles, \indexit{405}
  `PermutationsList', 151
  `PermutationTom', 707
  `Permuted', 201
    \sub as a permutation action, 399
    \sub for class functions, 773
  `PGL', 515
  `PGU', 515
  `Phi', 138
  point stabilizer, 401
  Polycyclic Generating Systems, \indexit{435}
  `PolynomialByExtRep', 689
  `PolynomialByExtRepNC', 689
  `PolynomialCoefficientsOfPolynomial', 674
  `PolynomialDivisionAlgorithm', 685
  Polynomial Factorization, \indexit{677}
  `PolynomialModP', 677
  `PolynomialReducedRemainder', 685
  `PolynomialReduction', 684
  `PolynomialRing', 680
  Polynomial Rings, \indexit{680}
  Polynomials as Univariate Polynomials in one Indeterminate, \indexit{674}
  polynomials over abelian number fields, factors, 592
  Polynomials over the Rationals, \indexit{677}
  `PopOptions', 88
  Portability, \indexit{90}
  Porting GAP, \indexit{839}
  `Position', 190
  `PositionBound', 192
  `PositionCanonical', 191
  `PositionFirstComponent', 193
  `PositionNonZero', 193
  `PositionNot', 193
  `PositionNthOccurrence', 191
  `PositionProperty', 192
  `Positions', 191
  `PositionSet', 192
  `PositionsOp', 191
  `PositionSorted', 191
  `PositionStream', 100
  `PositionSublist', 193
  `PositionWord', 334
  `PositiveIntegers', 126
  positive number, 48
  `PositiveRoots', 646
  `PositiveRootVectors', 646
  `PossibleClassFusions', 808
  `PossibleFusionsCharTableTom', 720
  Possible Permutation Characters, \indexit{792}
  possible permutation characters, 792, 795
  `PossiblePowerMaps', 802
  power, 48
    \sub matrix, 224
    \sub meaning for class functions, 772
    \sub of words, 334
  `PowerMap', 802
  `PowerMapByComposition', 804
  `PowerMapOp', 802
  Power Maps, \indexit{801}
  `PowerMapsAllowedBySymmetrizations', 819
  `PowerMod', 571
  `PowerModCoeffs', 220
  `PowerModInt', 131
  `PowerPartition', 155
  powerset, 149
  `PowerSubalgebraSeries', 623
  `PQuotient', 476
  precedence, 48
  precedence test, for permutations, 412
  `PrefrattiniSubgroup', 363
    \sub for groups with pcgs, 450
  `PreImage', 308
  `PreImageElm', 308
  `PreImages', 308
  `PreImagesElm', 307
  Preimages in the Free Group, \indexit{464}
  Preimages in the Free Semigroup, \indexit{550}
  `PreimagesOfTransformation', 555
  `PreImagesRange', 307
  `PreImagesRepresentative', 308
  `PreImagesSet', 308
  Preimages under Homomorphisms from an FpGroup, \indexit{475}
  Preimages under Mappings, \indexit{307}
  preorder, 315
  `PresentationFpGroup', 481
  `PresentationNormalClosure', 486
  `PresentationNormalClosureRrs', 486
  `PresentationSubgroup', 484
  `PresentationSubgroupMtc', 485
  `PresentationSubgroupRrs', 484
  `PresentationViaCosetTable', 482
  previous result, 64
  `PrevPrimeInt', 132
  `PrimaryGeneratorWords', 485
  primary subgroup generators, 499
  `PrimeBlocks', 741
  `PrimeBlocksOp', 741
  `PrimeField', 579
  Prime Integers and Factorization, \indexit{131}
  `PrimePGroup', 368
  `PrimePowersInt', 134
  prime residue group, 138
    \sub exponent, 139
    \sub generator, 140
    \sub order, 138
  Prime Residues, \indexit{138}
  `PrimeResidues', function, 138
  `Primes', 131
  primitive, 407
  `PRIMITIVE_INDICES_MAGMA', 528
  `PrimitiveElement', 579
  `PrimitiveGroup', 527
  Primitive Groups, \indexit{417}
  `PrimitiveGroupsIterator', 527
  `PrimitiveIdentification', 528
  `PrimitiveIndexIrreducibleSolvableGroup', 529
  Primitive Permutation Groups, \indexit{526}
  `PrimitivePolynomial', 677
  `PrimitiveRoot', 587
  `PrimitiveRootMod', 140
  primitive root modulo an integer, 140
  Primitive Roots and Discrete Logarithms, \indexit{139}
  Primitivity of Characters, \indexit{824}
  `Print', 66
  `PrintAmbiguity', 815
  `PrintArray', 228
  `PrintCharacterTable', 750
  `PrintFactorsInt', 134
  `PrintFormattingStatus', 102
  Printing, Viewing and Displaying Finite Field Elements, \indexit{589}
  Printing Character Tables, \indexit{747}
  Printing Class Functions, \indexit{773}
  Printing Presentations, \indexit{487}
  Printing Tables of Marks, \indexit{705}
  `PrintObj', 67
    \sub for character tables, 747, 773
    \sub for tables of marks, 705
  `PrintTo', 95
    \sub for streams, 101
  `ProbabilityShapes', 678
  problems, 836
  Problems on Particular Systems, \indexit{838}
  procedure call, 50
  Procedure Calls, \indexit{50}
  procedure call with arguments, 50
  `Process', 107
  Process, \indexit{107}
  `PROD_GF2MAT_GF2MAT_ADVANCED', 238
  `PROD_GF2MAT_GF2MAT_SIMPLE', 238
  `Product', 204
  product, of words, 334
    \sub rational functions, 670
  `ProductCoeffs', 220
  `ProductOfStraightLinePrograms', 342
  `ProductSpace', 623
  `ProductX', 206
  `ProfileFunctions', 83
  `ProfileGlobalFunctions', 83
  `ProfileMethods', 82
  `ProfileOperations', 82
  `ProfileOperationsAndMethods', 82
  `PROFILETHRESHOLD', 83
  Profiling, \indexit{82}
  `ProjectedInducedPcgs', 443
  `ProjectedPcElement', 443
  `Projection', 305
    \sub example for direct products, 504
    \sub example for semidirect products, 506
    \sub example for subdirect products, 507
    \sub example for wreath products, 507
    \sub for group products, 509
  `ProjectionMap', 811
  projections, find all, 393
  `ProjectiveActionHomomorphismMatrixGroup', 430
  `ProjectiveActionOnFullSpace', 430
  `ProjectiveGeneralLinearGroup', 515
  `ProjectiveGeneralUnitaryGroup', 515
  `ProjectiveOrder', 237
  `ProjectiveSpecialLinearGroup', 515
  `ProjectiveSpecialUnitaryGroup', 515
  `ProjectiveSymplecticGroup', 515
  prompt, 64
    \sub partial, 64
  Properties, \indexit{124}
  Properties and Attributes for Lists, \indexit{193}
  Properties and Attributes of (General) Mappings, \indexit{305}
  Properties and Attributes of Binary Relations, \indexit{314}
  Properties and Attributes of Matrices, \indexit{225}
  Properties and Attributes of Rational Functions, \indexit{671}
  Properties and basic functionality, \indexit{281}
  Properties of a Lie Algebra, \indexit{644}
  Properties of rewriting systems, \indexit{346}
  Properties of Rings, \indexit{566}
  Properties of Tables of Marks, \indexit{711}
  `PRump', 364
  `PseudoRandom', 277
  `PSL', 515
  `PSP', 515
  `PSp', 515
  `PSU', 515
  `PthPowerImage', 650
  `PthPowerImages', 650
  Pure p-adic Numbers, \indexit{693}
  `PurePadicNumberFamily', 693
  `PushOptions', 88
\letter Q
  `Quadratic', 164
  quadratic residue, 141
  `QuaternionAlgebra', 618
  `QUIET', 850
  `QUIT', emergency quit, 73
  quit, in emergency, 73
  `quit', 68
  `QUITTING', 73
  `QuoInt', 129
  `Quotient', 562
  quotient, for finitely presented groups, 463
    \sub matrices, 224
    \sub matrix and matrix list, 225
    \sub matrix and scalar, 224
    \sub of free monoid, 551
    \sub of free semigroup, 549
    \sub of words, 334
    \sub rational functions, 670
    \sub scalar and matrix, 224
    \sub scalar and matrix list, 225
    \sub vector and matrix, 224
  `QuotientFromSCTable', 617
  Quotient Methods, \indexit{476}
  `QuotientMod', 571
  `QuotientPolynomialsExtRep', 690
  `QuotientRemainder', 570
  Quotients, \indexit{541}
  Quotients and Remainders, \indexit{129}
  `QuotientSemigroupCongruence', 541
  `QuotientSemigroupHomomorphism', 541
  `QuotientSemigroupPreimage', 541
  `QuotRemLaurpols', 679
\letter R
  $r_N$, 162
  `RadicalGroup', 363
  `RadicalOfAlgebra', 626
  `Random', 136
    \sub `[coll]', 276
    \sub for integers, 129
    \sub for rationals, 146
  `RandomBinaryRelationOnPoints', 316
  random element, of a list or collection, 276
  Random Elements, \indexit{276}
  `RandomInvertibleMat', 229
  `RandomIsomorphismTest', 461
  Random Isomorphism Testing, \indexit{461}
  Randomized Methods for Permutation Groups, \indexit{419}
  `RandomList', 277
  `RandomMat', 229
  Random Matrices, \indexit{229}
  `RandomPrimitivePolynomial', 589
  random seed, 277
  `RandomSource', 137
  Random Sources, \indexit{136}
  `RandomTransformation', 554
  `RandomUnimodularMat', 229
  `Range', 306
  range, 206
  Ranges, \indexit{206}
  `RankAction', 406
  `RankFilter', 117
  `RankMat', 229
  `RankOfTransformation', 555
  `RankPGroup', 368
  `Rat', 146
    \sub for strings, 257
  `RationalClass', 360
  `RationalClasses', 361
  `RationalFunctionByExtRep', 689
  `RationalFunctionByExtRepNC', 689
  `Rational\-Function\-By\-Ext\-Rep\-With\-Cancellation', 690
  Rational Function Families, \indexit{686}
  `RationalFunctionsFamily', 686
  `RationalizedMat', 165
  `Rationals', 145
  `RClassOfHClass', 542
  `Read', 94
    \sub for streams, 99
  `ReadAll', 99
  `ReadAllLine', 105
  `ReadAsFunction', 94
    \sub for streams, 99
  `ReadByte', 99
  read eval print loop, 64
  `ReadLine', 99
  `ReadPackage', 846
  `ReadPkg', 849
  `ReadTest', 84
    \sub for streams, 99
  `RealClasses', 739
  `RealizableBrauerCharacters', 799
  `RecNames', 261
  Recognizing Characters, \indexit{253}
  record, component access, 262
    \sub component assignment, 262
    \sub component variable, 262
    \sub component variable assignment, 263
  Record Access Operations, \indexit{266}
  Record Assignment, \indexit{262}
  record assignment, operation, 266
  record boundness test, operation, 266
  record component, operation, 266
  record unbind, operation, 266
  Recovery from NoMethodFound-Errors, \indexit{77}
  recursion, 55
  redisplay a help section, 23
  redisplay with next help viewer, 23
  `ReduceCoeffs', 220
  `ReduceCoeffsMod', 220
  `ReducedAdditiveInverse', 345
  `ReducedCharacters', 783
  `ReducedClassFunctions', 782
  `ReducedComm', 345
  `ReducedConfluentRewritingSystem', 552
  `ReducedConjugate', 345
  `ReducedDifference', 345
  `ReducedForm', 344
  `ReducedGroebnerBasis', 686
  `ReducedInverse', 345
  `ReducedLeftQuotient', 345
  `ReducedOne', 345
  `ReducedPcElement', 438
  `ReducedPower', 345
  `ReducedProduct', 345
  `ReducedQuotient', 345
  `ReducedScalarProduct', 345
  `ReducedSum', 345
  `ReducedZero', 345
  `ReduceRules', 345
  `ReduceStabChain', 425
  Reducing Virtual Characters, \indexit{782}
  `Ree', 512
  `ReeGroup', 512
  `ReesCongruenceOfSemigroupIdeal', 540
  `ReesMatrixSemigroup', 543
  `ReesMatrixSemigroupElement', 544
  Rees Matrix Semigroups, \indexit{543}
  `ReesZeroMatrixSemigroup', 543
  `ReesZeroMatrixSemigroupElement', 544
  `ReesZeroMatrixSemigroupElementIsZero', 544
  `RefinedPcGroup', 456
  `ReflectionMat', 228
  `ReflexiveClosureBinaryRelation', 316
  reflexive relation, 314
  regular, 406
  regular action, 403
  `RegularActionHomomorphism', 404
  `RegularModule', 753
  relations, 303
  Relations Between Domains, \indexit{297}
  `RelationsOfFpSemigroup', 550
  `RelativeBasis', 602
  `RelativeBasisNC', 602
  relatively prime, 48
  `RelativeOrderOfPcElement', 438
  `RelativeOrders', of a pcgs, 437
  Relators in a Presentation, \indexit{487}
  `RelatorsOfFpGroup', 464
  remainder, operation, 296
  remainder of a quotient, 129
  `RemInt', 129
  `Remove', 177
  remove, an element from a set, 197
  `RemoveCharacters', 255
  `RemoveFile', 96
  `RemoveOuterCoeffs', 218
  `RemoveRelator', 489
  `RemoveSet', 197
  `RemoveStabChain', 425
  Repeat, \indexit{52}
  `repeat' loop, 52
  `ReplacedString', 255
  Representation, \indexit{120}
  representation, as a sum of two squares, 144
  Representations for Associative Words, \indexit{336}
  Representations for Group Homomorphisms, \indexit{395}
  Representations given by modules, \indexit{753}
  Representations of Algebras, \indexit{631}
  `RepresentationsOfObject', 121
  `Representative', 273
  representative, of a list or collection, 274
  `RepresentativeAction', 402
  `RepresentativeLinearOperation', 631
  `RepresentativeOperation', 849
  `RepresentativesContainedRightCosets', 358
  `RepresentativesFusions', 809
  `RepresentativeSmallest', 274
  `RepresentativesMinimalBlocks', 407
  `RepresentativesPerfectSubgroups', 376
  `RepresentativesPowerMaps', 804
  `RepresentativesSimpleSubgroups', 376
  `RepresentativeTom', 719
  `RepresentativeTomByGenerators', 719
  `RepresentativeTomByGeneratorsNC', 719
  `RequirePackage', 849
  `Reread', 96
  `REREADING', 96
  `RereadPackage', 846
  `RereadPkg', 849
  `Reset', 136
  `ResetOptionsStack', 88
  residue, quadratic, 141
  Residue Class Rings, \indexit{134}
  `RespectsAddition', 311
  `RespectsAdditiveInverses', 311
  `RespectsInverses', 310
  `RespectsMultiplication', 310
  `RespectsOne', 310
  `RespectsScalarMultiplication', 311
  `RespectsZero', 311
  `RestoreStateRandom', 276
  Restricted and Induced Class Functions, \indexit{781}
  `RestrictedClassFunction', 781
  `RestrictedClassFunctions', 781
  Restricted Lie algebras, \indexit{649}
  `RestrictedMapping', 305
  `RestrictedPartitions', 154
  `RestrictedPerm', 414
  `RestrictedPermNC', 414
  `RestrictedTransformation', 555
  `RestrictOutputsOfSLP', 341
  `Resultant', 675
  `ResultOfStraightLineProgram', 339
  Return, \indexit{58}
  `return', 68
    \sub no value, 58
    \sub with value, 58
  `ReturnFail', 63
  `ReturnFalse', 63
  return from break loop, 68
  `ReturnTrue', 63
  `Reversed', 199
  `RewindStream', 100
  `RewriteWord', 470
  Rewriting in Groups and Monoids, \indexit{346}
  Rewriting Systems and the Knuth-Bendix Procedure, \indexit{552}
  `RightActingAlgebra', 634
  `RightActingRingOfIdeal', 565
  `RightAlgebraModule', 632
  `RightAlgebraModuleByGenerators', 632
  `RightCoset', 356
  `RightCosets', 357
  right cosets, 356
  `RightCosetsNC', 357
  `RightDerivations', 641
  `RightIdeal', 563
  `RightIdealByGenerators', 564
  `RightIdealNC', 564
  `RightModuleByHomomorphismToMatAlg', 635
  `RightShiftRowVector', 218
  `RightTransversal', 357
  `Ring', 561
  `RingByGenerators', 562
  Ring Homomorphisms, \indexit{312}
  Rings With One, \indexit{565}
  `RingWithOne', 565
  `RingWithOneByGenerators', 566
  `RNamObj', 266
  root, of 1 modulo an integer, 142
    \sub of an integer, 128
    \sub of an integer, smallest, 128
    \sub of an integer modulo another, 141
  `RootInt', 128
  `RootMod', 141
  `RootOfDefiningPolynomial', 579
  `RootsMod', 141
  Roots Modulo Integers, \indexit{140}
  roots of unity, 157
  `RootsOfUPol', 674
  `RootsUnityMod', 142
  `RootSystem', 646
  `RoundCyc', 159
  Row and Matrix Spaces, \indexit{606}
  `RowIndexOfReesMatrixSemigroupElement', 544
  `Row\-Index\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 544
  row spaces, 606
  Row Vectors over Finite Fields, \indexit{216}
  `Rules', 344
  Running GAP under MacOS, \indexit{31}
  `Runtime', 82
  `Runtimes', 81
\letter S
  $s_N$, 162
  `SameBlock', 742
  `SandwichMatrixOfReesMatrixSemigroup', 544
  `SandwichMatrixOfReesZeroMatrixSemigroup', 544
  save, 37
  `SaveOnExitFile', 73
  `SaveWorkspace', 37
  Saving and Loading a Workspace, \indexit{37}
  Saving a Pc Group, \indexit{457}
  saving on exit, 73
  `ScalarProduct', for characters, 777
  Schreier, 484
  Schreier-Sims, random, 419
  `SchurCover', 382
  Schur Covers and Multipliers, \indexit{382}
  Schur multiplier, 382
  scope, 43
  `ScriptFromString', 716
  Searching for Homomorphisms, \indexit{393}
  `SecHMSM', 259
  secondary subgroup generators, 499
  `SecondsDMYhms', 259
  `SeekPositionStream', 100
  Selecting a Different MeatAxe, \indexit{697}
  Selection Functions, \indexit{517}
  `SemidirectProduct', 505
  Semidirect Products, \indexit{505}
  `SemiEchelonBasis', 608
  `SemiEchelonBasisNC', 608
  `SemiEchelonMat', 231
  `SemiEchelonMatDestructive', 232
  `SemiEchelonMats', 232
  `SemiEchelonMatsDestructive', 232
  `SemiEchelonMatTransformation', 232
  `Semigroup', 538
  semigroup, 538
  `SemigroupByGenerators', 538
  `SemigroupByMultiplicationTable', 539
  `SemigroupIdealByGenerators', 540
  `SemigroupOfRewritingSystem', 553
  semiregular, 406
  Semisimple Lie Algebras and Root Systems, \indexit{645}
  `SemiSimpleType', 645
  sequence, Bernoulli, 148
    \sub Fibonacci, 155
    \sub Lucas, 156
  Series of Ideals, \indexit{643}
  `Set', 270
  `SetAssertionLevel', 81
  `SetCommutator', 455
  `SetConjugate', 455
  `SetCrystGroupDefaultAction', 434
  set difference, of collections, 275
  `SetEntrySCTable', 616
  `SetGasmanMessageStatus', 87
  `SetHelpViewer', 24
  `SetIndeterminateName', 669
  `SetInfoLevel', 80
  `SetName', 114
  Set Operations via Boolean Lists, \indexit{211}
  `SetParent', 290
  `SetPower', 455
  `SetPrintFormattingStatus', 102
  `SetRecursionTrapInterval', 86
  `SetReducedMultiplication', 464
  Sets, \indexit{110}
  sets, 172, 196
  Sets of Subgroups, \indexit{373}
  set stabilizer, 401
  `Setter', 122
  setter, 122
  Setter and Tester for Attributes, \indexit{122}
  `SetX', 206
  `ShallowCopy', 113
    \sub for lists, 180
  `ShiftedCoeffs', 220
  `ShiftedPadicNumber', 693
  Shifting and Trimming Coefficient Lists, \indexit{218}
  `ShortestVectors', 247
  `ShortLexOrdering', 283
  short vectors spanning a lattice, 245, 783
  `ShowArgument', 77
  `ShowArguments', 77
  `ShowDetails', 77
  `ShowImpliedFilters', 118
  `ShowMethods', 78
  `ShowOtherMethods', 78
  `ShrinkAllocationPlist', 182
  `ShrinkAllocationString', 252
  `ShrinkCoeffs', 221
  `ShrinkRowVector', 218
  `SiftedPcElement', 438
  `SiftedPermutation', 424
  `SiftedVector', 609
  `Sigma', 142
  sign, of an integer, 127
  Sign and Cycle Structure, \indexit{413}
  `SignInt', 127
  `SignPartition', 154
  `SignPerm', 413
  `SimpleLieAlgebra', 641
  `SimpleSystem', 646
  `SimplifiedFpGroup', 483
  SimplifiedFpGroup, \indexit{483}
  `SimplifyPresentation', 490
  `SimsNo', 528
  `SimultaneousEigenvalues', 238
  `SingleCollector', 455
  singlequote character, 251
  singlequotes, 249
  `SINT_CHAR', 257
  `Size', 273
    \sub for character tables, 735
    \sub for groups with pcgs, 450
  size, of a list or collection, 273
  `SizeBlist', 211
  `SizeConsiderFunction', 378
  `SizeNumbersPerfectGroups', 523
  `SizeOfFieldOfDefinition', 799
  `SizesCentralizers', 736
  `SizesConjugacyClasses', 736
  `SizeScreen', 76
  SizeScreen, \indexit{76}
  `SizesPerfectGroups', 522
  `SizeStabChain', 423
  `SL', 513
  smaller, associative words, 333
    \sub elements of finitely presented groups, 464
    \sub nonassociative words, 327
    \sub pcwords, 453
    \sub rational functions, 671
  `SmallerDegreePermutationRepresentation', 416
  smaller or equal, 47
  smaller test, 47
  `SmallestGeneratorPerm', 412
  `SmallestMovedPoint', 412
  `SmallestRootInt', 128
  `SmallGeneratingSet', 379
  `SmallGroup', 520
  Small Groups, \indexit{519}
  `SmallGroupsInformation', 521
  Smash MeatAxe Flags, \indexit{701}
  smith normal form, 850
  `SmithNormalFormIntegerMat', 242
  `SmithNormalFormIntegerMatTransforms', 242
  `SMTX.AbsoluteIrreducibilityTest', 700
  `SMTX.AlgEl', 701
  `SMTX.AlgElCharPol', 701
  `SMTX.AlgElCharPolFac', 701
  `SMTX.AlgElMat', 701
  `SMTX.AlgElNullspaceDimension', 701
  `SMTX.AlgElNullspaceVec', 701
  `SMTX.CentMat', 701
  `SMTX.CentMatMinPoly', 701
  `SMTX.CompleteBasis', 700
  `SMTX.Getter', 700
  `SMTX.GoodElementGModule', 700
  `SMTX.IrreducibilityTest', 700
  `SMTX.MatrixSum', 700
  `SMTX.MinimalSubGModule', 700
  `SMTX.MinimalSubGModules', 700
  `SMTX.RandomIrreducibleSubGModule', 700
  `SMTX.Setter', 700
  `SMTX.SortHomGModule', 700
  `SMTX.Subbasis', 701
  `SO', 514
  `Socle', 364
  `SocleTypePrimitiveGroup', 417
  `SolutionIntMat', 240
  `SolutionMat', 230
  `SolutionMatDestructive', 230
  `SolutionNullspaceIntMat', 240
  Some Remarks about Character Theory in GAP, \indexit{724}
  Some Special Algebras, \indexit{618}
  `Sort', 195
  `SortedCharacters', 760
  `SortedCharacterTable', 761
  Sorted Character Tables, \indexit{760}
  `SortedList', 270
  sorted list, 194
  Sorted Lists and Sets, \indexit{196}
  sorted lists as collections, 268
  `SortedSparseActionHomomorphism', 403
  `SortedTom', 706
  `Sortex', 195
  Sorting Lists, \indexit{195}
  `SortingPerm', 196
  Sorting Tables of Marks, \indexit{706}
  `SortParallel', 195
  `Source', 306
  `SourceOfIsoclinicTable', 759
  `SP', 514
  `Sp', 514
  space, 41
  `SparseActionHomomorphism', 403
  `SparseCartanMatrix', 647
  Special Characters, \indexit{251}
  special character sequences, 251
  Special Filenames, \indexit{93}
  Special Generating Sets, \indexit{379}
  `SpecialLinearGroup', 513
  Special Multiplication Algorithms for Matrices over GF(2), \indexit{238}
  `SpecialOrthogonalGroup', 514
  Special Pcgs, \indexit{447}
  `SpecialPcgs', attribute, 447
  Special Rules for Input Lines, \indexit{65}
  `SpecialUnitaryGroup', 514
  Specific and Parametrized Subgroups, \indexit{362}
  Specific Methods for Subgroup Lattice Computations, \indexit{376}
  `SplitCharacters', 755
  `SplitExtension', 459
  `SplitExtensions', 460
  `SplitString', 254
  `SplittingField', 673
  `Sqrt', 296
  square root, of an integer, 128
  `SquareRoots', 324
  `SSortedList', 270
  `StabChain', 421
  `StabChainBaseStrongGenerators', 422
  `StabChainImmutable', 421
  `StabChainMutable', 421
  `StabChainOp', 421
  `StabChainOptions', 422
  `Stabilizer', 401
  Stabilizer Chain Records, \indexit{422}
  Stabilizer Chains, \indexit{418}
  `StabilizerOfExternalSet', 409
  `StabilizerPcgs', 450
  Stabilizers, \indexit{401}
  `StandardAssociate', 568
  `StandardGeneratorsFunctions', 716
  `StandardGeneratorsInfo', for groups, 715
    \sub for tables of marks, 720
  `StandardGeneratorsOfGroup', 717
  Standard Generators of Groups, \indexit{715}
  Standardization of coset tables, \indexit{469}
  `StandardizeTable', 469
  `StarCyc', 164
  `State', 136
  Statements, \indexit{49}
  `StateRandom', 276
  `Stirling1', 148
  `Stirling2', 149
  Stirling number of the first kind, 148
  Stirling number of the second kind, 149
  `StoredGroebnerBasis', 686
  `StoreFusion', 807
  Storing Normal Subgroup Information, \indexit{764}
  `StraightLineProgElm', 342
  `StraightLineProgGens', 343
  `StraightLineProgram', 338
  Straight Line Program Elements, \indexit{342}
  `StraightLineProgramNC', 338
  Straight Line Programs, \indexit{338}
  `StraightLineProgramsTom', 718
  `StreamsFamily', 98
  `StretchImportantSLPElement', 343
  strictly sorted list, 194
  `String', 254
    \sub for cyclotomics, 159
  `StringDate', 259
  `StringOfResultOfStraightLineProgram', 340
  `StringPP', 254
  strings, equality of, 253
    \sub inequality of, 253
    \sub lexicographic ordering of, 253
  String Streams, \indexit{104}
  `StringTime', 259
  `StrongGeneratorsStabChain', 424
  `StronglyConnectedComponents', 316
  <Struct>, 287
  `<Struct>ByGenerators', 288
  `StructuralCopy', 113
    \sub for lists, 180
  structure constant, 746, 747
  `StructureConstantsTable', 604
  `StructureDescription', 354
  Structure Descriptions, \indexit{354}
  `<Struct>WithGenerators', 288
  `SU', 514
  `Subalgebra', 619
  `SubAlgebraModule', 635
  `SubalgebraNC', 619
  Subalgebras, \indexit{619}
  `SubalgebraWithOne', 619
  `SubalgebraWithOneNC', 620
  `SubdirectProduct', 507
  Subdirect Products, \indexit{507}
  `SubdirectProducts', 507
  subdomains, 291
  `Subfield', 579
  `SubfieldNC', 579
  `Subfields', 579
  Subfields of Fields, \indexit{579}
  `Subgroup', 351
  `SubgroupByPcgs', 441
  `SubgroupByProperty', 352
  subgroup fusions, 805
  subgroup generators tree, 499
  Subgroup Lattice, \indexit{374}
  `SubgroupNC', 351
  `SubgroupOfWholeGroupByCosetTable', 470
  `SubgroupOfWholeGroupByQuotientSubgroup', 475
  Subgroup Presentations, \indexit{484}
  `SubgroupProperty', 426
  Subgroups, \indexit{351}
  subgroups, polyhedral, 746
  Subgroups characterized by prime powers, \indexit{365}
  Subgroup Series, \indexit{369}
  `SubgroupShell', 352
  Subgroups of Polycyclic Groups - Canonical Pcgs, \indexit{441}
  Subgroups of Polycyclic Groups - Induced Pcgs, \indexit{440}
  `SubgroupsSolvableGroup', 377
  sublist, 174
    \sub access, 174
    \sub assignment, 176
    \sub operation, 175
  sublist assignment, operation, 177
  `Submagma', 320
  `SubmagmaNC', 320
  `SubmagmaWithInverses', 320
  `SubmagmaWithInversesNC', 320
  `SubmagmaWithOne', 320
  `SubmagmaWithOneNC', 320
  `Submodule', 574
  `SubmoduleNC', 574
  Submodules, \indexit{574}
  `Submonoid', 545
  `SubmonoidNC', 545
  `SubnearAdditiveGroup', 559
  `SubnearAdditiveGroupNC', 559
  `SubnearAdditiveMagma', 559
  `SubnearAdditiveMagmaNC', 559
  `SubnearAdditiveMagmaWithZero', 559
  `SubnearAdditiveMagmaWithZeroNC', 559
  `SubnormalSeries', 369
  `Subring', 562
  `SubringNC', 562
  `SubringWithOne', 566
  `SubringWithOneNC', 566
  Subroutines for the Construction of Class Fusions, \indexit{820}
  Subroutines for the Construction of Power Maps, \indexit{818}
  `Subsemigroup', 538
  `SubsemigroupNC', 538
  subsets, 149
  subset test, for collections, 274
  `Subspace', 598
  `SubspaceNC', 598
  `Subspaces', 600
  `SubstitutedWord', 335
  `SubsTom', 708
  `Sub<struct>', 291
  `Sub<struct>NC', 291
  `SubSyllables', 336
  subtract, a set from another, 198
  `SubtractBlist', 212
  subtraction, 48
    \sub matrices, 223
    \sub matrix and scalar, 223
    \sub rational functions, 670
    \sub scalar and matrix, 223
    \sub scalar and matrix list, 225
    \sub scalar and vector, 215
    \sub vector and scalar, 215
    \sub vectors, 215
  `SubtractSet', 198
  `Subword', 334
  `Successors', 315
  Suitability for Compilation, \indexit{36}
  `Sum', 204
  Sum and Intersection of Pcgs, \indexit{446}
  `SumFactorizationFunctionPcgs', 446
  `SumIntersectionMat', 233
  `SumX', 206
  `SupersolvableResiduum', 364
  `support', email address, 837
  `SupportedCharacterTableInfo', 728
  `SurjectiveActionHomomorphismAttr', 410
  `SuzukiGroup', 512
  `SylowComplement', 364
  `SylowSubgroup', 364
  Sylow Subgroups and Hall Subgroups, \indexit{364}
  `SylowSystem', 365
  Symbols, \indexit{40}
  Symmetric and Alternating Groups, \indexit{416}
  `SymmetricClosureBinaryRelation', 316
  `SymmetricGroup', 512
  symmetric group, powermap, 155
  `SymmetricParentGroup', 417
  `SymmetricParts', 789
  `SymmetricPowerOfAlgebraModule', 660
  symmetric relation, 315
  `Symmetrizations', 788
  symmetrizations, orthogonal, 789, 790
    \sub symplectic, 790
  Symmetrizations of Class Functions, \indexit{788}
  `SymplecticComponents', 790
  `SymplecticGroup', 514
  syntax errors, 64
  system getter, 121
  system setter, 121
  `Sz', 512
\letter T
  $t_N$, 162
  `TableAutomorphisms', 763
  table automorphisms, 809, 821
  table of chapters for help books, 23
  `TableOfMarks', 703
  `TableOfMarksByLattice', 704
  `TableOfMarksComponents', 707
  `TableOfMarksCyclic', 722
  `TableOfMarksDihedral', 722
  `TableOfMarksFamily', 707
  `TableOfMarksFrobenius', 722
  Table of Marks Objects in GAP, \indexit{703}
  table of sections for help books, 23
  tables, 724, 726
  tabulator, 41
  `Tau', 142
  Technical Details about Tables of Marks, \indexit{707}
  Technical Details about the Implementation of Magma Rings, \indexit{666}
  Technical Matters Concerning General Mappings, \indexit{312}
  `TemporaryGlobalVarName', 46
  `Tensored', 780
  `TensorProductGModule ', 696
  `TensorProductOfAlgebraModules', 659
  Tensor Products and Exterior and Symmetric Powers, \indexit{659}
  test, for a primitive root, 140
    \sub for a rational, 145
    \sub for records, 261
    \sub for set equality, 197
  `TestConsistencyMaps', 814
  `Tester', 122
  tester, 122
  Test Files, \indexit{84}
  `TestHomogeneous', 824
  `TestInducedFromNormalSubgroup', 826
  Testing Finiteness of Finitely Presented Groups, \indexit{479}
  Testing for the System Architecture, \indexit{35}
  Testing Monomiality, \indexit{826}
  `TestJacobi', 616
  `TestMonomial', 826
  `TestMonomialQuick', 827
  `TestMonomialUseLattice', 827
  Test of the installation, \indexit{833}
  `TestPackageAvailability', 847
  `TestPerm1', 796
  `TestPerm2', 796
  `TestPerm3', 796
  `TestPerm4', 796
  `TestPerm5', 796
  `TestQuasiPrimitive', 825
  `TestRelativelySM', 828
  Tests for Actions, \indexit{406}
  Tests for the Availability of Methods, \indexit{383}
  `TestSubnormallyMonomial', 828
  The .gaprc file, \indexit{33}
  The Adjoint Representation, \indexit{651}
  The Compiler, \indexit{35}
  The Defining Attributes of Rational Functions, \indexit{688}
  The Dixon-Schneider Algorithm, \indexit{753}
  The Documentation, \indexit{835}
  The External Representation for Associative Words, \indexit{338}
  The family pcgs, \indexit{453}
  The Interface between Character Tables and Groups, \indexit{730}
  The Interface between Tables of Marks and Character Tables, \indexit{720}
  The Library of Tables of Marks, \indexit{723}
  `then', 51
  The Natural Action, \indexit{415}
  The Pager Command, \indexit{25}
  The Permutation Image of an Action, \indexit{402}
  The Representations of Rational Functions, \indexit{687}
  The Smash MeatAxe, \indexit{700}
  The Syntax in BNF, \indexit{59}
  `ThreeGroup' library, 520
  Tietze Options, \indexit{502}
  Tietze Transformations, \indexit{489}
  Tietze Transformations that introduce new Generators, \indexit{494}
  `TietzeWordAbstractWord', 487
  `time', 82
  Timing, \indexit{81}
  Todd-Coxeter Procedure, \indexit{553}
  `Trace', 226
    \sub for field elements, 581
    \sub of a matrix, 226
  `TracedCosetFpGroup', 467
  `TraceImmediateMethods', 79
  `TraceMat', 226
  `TraceMethods', 79
  `TracePolynomial', 580
  Tracing generator images through Tietze transformations, \indexit{497}
  Tracing Methods, \indexit{79}
  `TransferDiagram', 814
  `Transformation', 554
  `TransformationData', 554
  `TransformationFamily', 554
  `TransformationNC', 554
  `TransformationRelation', 556
  `TransformationType', 554
  `TransformingPermutations', 763
  `TransformingPermutationsCharacterTables', 763
  transitive, 406
  `TransitiveClosureBinaryRelation', 316
  `TransitiveGroup', 518
  `TransitiveIdentification', 518
  Transitive Permutation Groups, \indexit{518}
  transitive relation, 315
  `Transitivity', for characters, 779
    \sub for class functions, 779
    \sub for group actions, 406
  `TranslatorSubalgebra', 638
  transporter, 402
  `TransposedMat', 227
  `TransposedMatAttr', 227
  `TransposedMatDestructive', 228
  `TransposedMatImmutable', 227
  `TransposedMatMutable', 227
  `TransposedMatOp', 227
  `TransposedMatrixGroup', 429
  Transversals, \indexit{357}
  Triangular Matrices, \indexit{234}
  `TriangulizedIntegerMat', 241
  `TriangulizedIntegerMatTransform', 241
  `TriangulizedNullspaceMat', 229
  `TriangulizedNullspaceMatDestructive', 229
  `TriangulizeIntegerMat', 241
  `TriangulizeMat', 229
  `TrivialCharacter', 775
  `TrivialGroup', 510
  `TrivialIterator', 279
  `TrivialSubalgebra', 620
  `TrivialSubgroup', 362
  `TrivialSubmagmaWithOne', 324
  `TrivialSubmodule', 574
  `TrivialSubmonoid', 545
  `TrivialSubnearAdditiveMagmaWithZero', 559
  `TrivialSubspace', 599
  `TryCosetTableInWholeGroup', 470
  `TryGcdCancelExtRepPolynomials', 690
  `Tuples', 151
  tuple stabilizer, 401
  `TwoClosure', 426
  `TwoCoboundaries', 458
  `TwoCocycles', 458
  `TwoCohomology', 458
  `TwoGroup' library, 520
  `TwoSidedIdeal', 563
  `TwoSidedIdealByGenerators', 564
  `TwoSidedIdealNC', 564
  `TwoSquares', 144
  type, boolean, 169
    \sub cyclotomic, 157
    \sub records, 261
    \sub strings, 249
  `TypeObj', 125
  `TypeOfDefaultGeneralMapping', 313
  Types, \indexit{125}
  `TzEliminate', 492
  `TzFindCyclicJoins', 493
  `TzGo', 490
  `TzGoGo', 491
  `TzImagesOldGens', 498
  `TzInitGeneratorImages', 497
  `TzNewGenerator', 489
  `TzOptions', 502
  `TzPreImagesNewGens', 498
  `TzPrint', 488
  `TzPrintGeneratorImages', 498
  `TzPrintGenerators', 487
  `TzPrintLengths', 488
  `TzPrintOptions', 503
  `TzPrintPairs', 488
  `TzPrintPresentation', 488
  `TzPrintRelators', 487
  `TzPrintStatus', 488
  `TzSearch', 492
  `TzSearchEqual', 493
  `TzSort', 481
  `TzSubstitute', 494
  `TzSubstituteCyclicJoins', 497
\letter U
  $u_N$, 162
  `UglyVector', 612
  `Unbind', 44
    \sub for lists, 178
  `UnbindGlobal', 45
  `UnderlyingCharacteristic', 737
  `UnderlyingCharacterTable', 769
  `UnderlyingElement', fp group elements, 465
    \sub fp semigroup elements, 551
  `Underlying\-Element\-Of\-Rees\-Matrix\-Semigroup\-Element', 544
  `Underlying\-Element\-Of\-Rees\-Zero\-Matrix\-Semigroup\-Element', 544
  `UnderlyingExternalSet', 410
  `UnderlyingFamily', 640
  `UnderlyingGeneralMapping', 306
  `UnderlyingGroup', for character tables, 731
    \sub for tables of marks, 709
  `UnderlyingLeftModule', 602
  `UnderlyingLieAlgebra', 646
  `UnderlyingMagma', 663
  `UnderlyingRelation', 306
  `UnInstallCharReadHookFunc', 106
  `Union', 275
  union, of collections, 275
    \sub of sets, 197
  `Union2', 275
  `UnionBlist', 211
  `Unique', 199
  `UniteBlist', 212
  `UniteBlistList', 212
  `UniteSet', 197
  `Units', 567
  Units and Factorizations, \indexit{567}
  `UnivariatenessTestRationalFunction', 674
  `UnivariatePolynomial', 673
  `UnivariatePolynomialByCoefficients', 673
  `UnivariatePolynomialRing', 682
  Univariate Polynomial Rings, \indexit{682}
  Univariate Polynomials, \indexit{673}
  `Univariate\-Rational\-Function\-By\-Coefficients', 679
  Univariate Rational Functions, \indexit{679}
  `UniversalEnvelopingAlgebra', 652
  Universal Enveloping Algebras, \indexit{652}
  UNIX, features, 27
    \sub options, 27
  `UNIXSelect', 98
  `Unknown', 167
  `UnloadSmallGroupsData', 521
  `UnorderedTuples', 150
  Unpacking, \indexit{831}
  `UnprofileFunctions', 83
  `UnprofileMethods', 83
  `until', 52
  `UntraceMethods', 79
  `UpdateMap', 812
  `UpEnv', 71
  `UpperCentralSeriesOfGroup', 371
  `UpperSubdiagonal', 234
  `UseBasis', 576
  `UseFactorRelation', 297
  Useful Categories for all Elements of a Family, \indexit{301}
  Useful Categories of Elements, \indexit{299}
  `UseIsomorphismRelation', 297
  User Streams, \indexit{103}
  `UseSubsetRelation', 297
  utilities for editing GAP files, 75
\letter V
  $v_N$, 162
  `Valuation', 693
  `Value', 676
  `ValueCochain', 655
  `ValueGlobal', 45
  `ValueMolienSeries', 792
  `ValueOption', 89
  `ValuePol', 220
  `ValuesOfClassFunction', 769
  Variable Access in a Break Loop, \indexit{71}
  Variables, \indexit{43}
  Vectors as coefficients of polynomials, \indexit{219}
  `VectorSpace', 598
  `Vector\-Space\-By\-Pcgs\-Of\-Elementary\-Abelian\-Group', 449
  Vector Space Homomorphisms, \indexit{609}
  Vector Spaces Handled By Nice Bases, \indexit{611}
  `vi', 75
  `View', 66
  View and Print, \indexit{66}
  `ViewObj', 67
    \sub for character tables, 747
    \sub for class functions, 773
    \sub for tables of marks, 705
  `vim', 75
  `VirtualCharacter', 774
  virtual character, 776
  virtual characters, 767
\letter W
  $w_N$, 162
  `WedgeGModule ', 696
  `WeekDay', 259
  `WeightLexOrdering', 283
  `WeightOfGenerators', 284
  `WeightsTom', 711
  `WeightVecFFE', 219
  `WeylGroup', 648
  `WeylOrbitIterator', 649
  `Where', 70
  While, \indexit{52}
  `while' loop, 52
  Whitespaces, \indexit{41}
  Why Class Functions?, \indexit{767}
  `WordAlp', 254
  words, in generators, 353
  Working with large degree permutation groups, \indexit{427}
  `WreathProduct', 507
  wreath product embedding, 508
  `WreathProductImprimitiveAction', 508
  `WreathProductOrdering', 285
  `WreathProductProductAction', 508
  Wreath Products, \indexit{507}
  `WriteAll', 101
  `WriteByte', 101
  `WriteLine', 101
\letter X
  $x_N$, 162
\letter Y
  $y_N$, 162
\letter Z
  `Z', 583
  `ZClassRepsQClass', 433
  `Zero', 293
  `ZeroAttr', 293
  `ZeroCoefficient', 664
  `ZeroCoefficientRatFun', 688
  `ZeroImmutable', 293
  `ZeroMapping', 305
  `ZeroMutable', 293
  `ZeroOp', 293
  `ZeroSameMutability', 293
  `ZeroSM', 293
  `ZippedProduct', 690
  `ZippedSum', 690
  `ZmodnZ', 135
  `ZmodnZObj', 135
  `ZmodpZ', 135
  `ZmodpZNC', 135
  `ZumbroichBase', 594
  `Zuppos', 376
