\letter A
  A typical library, \indexit{31}
  A-loop, 28
  About Cayley tables, \indexit{11}
  Acknowledgement, \indexit{5}
  Additional varieties of loops, \indexit{28}
  `AllSubloops', 19
  alternative loop, 26
  antiautomorphic inverse property, 25
  `AreEqualDiscriminators', 23
  `AsGroup', 15
  `AsLoop', 8, 14
  `AsQuasigroup', 8, 14
  associated left Bruck loop, 29
  Associativity, commutativity and generalizations, \indexit{25}
  `Associator', 17
  associator, 17
  associator subloop, 21
  Associators and commutators, \indexit{17}
  `AssociatorSubloop', 21
  `AssoicatedLeftBruckLoop', 29
  automorphic inverse property, 25
  `AutomorphismGroup', 23
\letter B
  Basic arithmetic operations, \indexit{16}
  Basic attributes, \indexit{16}
  Bol loop, 9
\letter C
  C-loop, 26
  Calculating with quasigroups, \indexit{9}
  Canonical and normalized Cayley tables, \indexit{11}
  `CanonicalCayleyTable', 11
  Cayley table, 11
  `CayleyTable', 16
  `CayleyTableByPerms', 13
  CC-loops, \indexit{32}
  `CCLoop', 33
  `Center', 21
  centrum, 21
  cocycle, 7
  code loop, 28
  Code loops, \indexit{32}
  `CodeLoop', 32
  `Commutant', 21
  commutant, 21
  `Commutator', 17
  commutator, 17
  Comparing quasigroups with common parent, \indexit{18}
  conjugacy closed loop, 27, 32
  Conjugacy closed loops and related properties, \indexit{27}
  conjugation, 20
  Conversions, \indexit{14}
  Conversions between magmas, quasigroups, loops and groups, \indexit{8}
  Core methods for Bol loops, \indexit{29}
  coset, 19
  Creating quasigroups and loops by extensions, \indexit{14}
  Creating quasigroups and loops by sections, \indexit{13}
  Creating quasigroups and loops from a file, \indexit{12}
  Creating quasigroups and loops manually, \indexit{11}
  cyclic modification, 29
\letter D
  `DerivedLength', 22
  `DerivedSubloop', 22
  diassociative loop, 25
  dihedral modification, 29
  `DirectProduct', 15
  `Discriminator', 23
  `DisplayLibraryInfo', 31
  distributive quasigroup, 26
  Documentation, \indexit{5}
\letter E
  `Elements', 16
  entropic quasigroup, 26
  `Exponent', 16
  exponent, 16
  extension of loops, 6
  Extensions, \indexit{6}
  extra loop, 26
\letter F
  Factor loops, \indexit{21}
  `FactorLoop', 21
  Feedback, \indexit{5}
  flexible loop, 26
  `FrattinifactorSize', 22
  `FrattiniSubloop', 22
\letter G
  Generators, \indexit{17}
  `GeneratorsOfLoop', 17
  `GeneratorsOfQuasigroup', 17
  `GeneratorsSmallest', 17
  group, 6
  group with triality, 29
  groupoid, 6
\letter H
  `HasAntiautomorphicInverseProperty', 25
  `HasAutomorphicInverseProperty', 25
  `HasInverseProperty', 25
  `HasLeftInverseProperty', 25
  `HasRightInverseProperty', 25
  `HasTwosidedInverses', 25
  `HasWeakInverseProperty', 25
  homomorphism, 6
  Homomorphisms and homotopisms, \indexit{6}
  homotopism, 6
  How are isomorphisms computed, \indexit{23}
\letter I
  idempotent quasigroup, 26
  identity element, 6
  identity of Bol-Moufang type, 26
  inner mapping group, 20
  Inner mapping groups, \indexit{20}
  `InnerMappingGroup', 20
  Installation, \indexit{5}
  Interesting loops, \indexit{33}
  `InterestingLoop', 33
  `Inverse', 17
  inverse, 17
  Inverse properties, \indexit{25}
  inverse property, 25
  `IsALoop', 28
  `IsAlternative', 27
  `IsAssociative', 25
  `IsCCLoop', 27
  `IsCLoop', 27
  `IsCodeLoop', 28
  `IsCommutative', 25
  `IsDiassociative', 25
  `IsDistributive', 26
  `IsEntropic', 26
  `IsExtraLoop', 27
  `IsFlexible', 27
  `IsIdempotent', 26
  `IsLCCLoop', 27
  `IsLCLoop', 27
  `IsLDistributive', 26
  `IsLeftALoop', 28
  `IsLeftAlternative', 27
  `IsLeftBolLoop', 27
  `IsLeftBruckLoop', 28
  `IsLeftDistributive', 26
  `IsLeftKLoop', 28
  `IsLeftNuclearSquareLoop', 27
  `IsLeftPowerAlternative', 27
  `IsLoopCayleyTable', 11
  `IsLoopTable', 11
  `IsMedial', 26
  `IsMiddleALoop', 28
  `IsMiddleNuclearSquareLoop', 27
  `IsMoufangLoop', 27
  `IsNilpotent', 22
  `IsNormal', 21
  `IsNuclearSquareLoop', 27
  `IsomorphicCopyByNormalSubloop', 23
  `IsomorphicCopyByPerm', 23
  isomorphism, 6
  `IsomorphismLoops', 22
  Isomorphisms and automorphisms, \indexit{22}
  `IsOsbornLoop', 28
  isotopism, 6
  `IsotopismLoops', 23
  Isotopisms, \indexit{23}
  `IsPowerAlternative', 27
  `IsPowerAssociative', 25
  `IsQuasigroupCayleyTable', 11
  `IsQuasigroupTable', 11
  `IsRCCLoop', 27
  `IsRCLoop', 27
  `IsRDistributive', 26
  `IsRightALoop', 28
  `IsRightAlternative', 27
  `IsRightBolLoop', 27
  `IsRightBruckLoop', 28
  `IsRightDistributive', 26
  `IsRightKLoop', 28
  `IsRightNuclearSquareLoop', 27
  `IsRightPowerAlternative', 27
  `IsSemisymmetric', 26
  `IsSimple', 21
  `IsSolvable', 22
  `IsSteinerLoop', 28
  `IsSteinerQuasigroup', 26
  `IsStronglyNilpotent', 22
  `IsSubloop', 19
  `IsSubquasigroup', 19
  `IsTotallySymmetric', 26
  `IsUnipotent', 26
  iterated centers, 22
  `ItpSmallLoop', 33
\letter K
  K-loop, 28
\letter L
  Latin square, 6, 11
  LC-loop, 26
  left A-loop, 28
  left alternative loop, 26
  left Bol loop, 26, 29
  Left Bol loops, \indexit{31}
  left Bruck loop, 28
  left conjugacy closed loop, 27
  left distributive quasigroup, 26
  left division, 16
  left inner mapping, 20
  left inner mapping group, 20
  left inverse, 17
  left inverse property, 25
  left multiplication group, 6
  left nuclear square loop, 26
  left nucleus, 21
  left power alternative loop, 27
  left section, 6
  left translation, 6
  `LeftBolLoop', 31
  `LeftDivision', 16
  `LeftDivisionCayleyTable', 17
  `LeftInnerMapping', 20
  `LeftInnerMappingGroup', 20
  `LeftInverse', 17
  `LeftMultiplicationGroup', 20
  `LeftNucleus', 21
  `LeftSection', 19
  `LeftTranslation', 19
  Libraries of loops up to isotopism, \indexit{33}
  `LibraryLoop', 31
  list of files, 35
  loop, 6
  loop table, 11
  `LoopByCayleyTable', 12
  `LoopByCyclicModification', 29
  `LoopByDihedralModification', 29
  `LoopByExtension', 14
  `LoopByLeftSection', 13
  `LoopByRightSection', 13
  `LoopFromFile', 12
  `LoopMG2', 29
  Loops of Bol-Moufang type, \indexit{26}
  loops of Bol-Moufang type, 26
  `LoopsUpToIsomorphism', 22
  `LoopsUpToIsotopism', 23
  lower central series, 22
  `LowerCentralSeries', 22
\letter M
  magma, 6
  medial quasigroup, 26
  middle A-loop, 28
  middle inner mapping, 20
  middle nuclear square loop, 26
  middle nucleus, 21
  `MiddleInnerMapping', 20
  `MiddleInnerMappingGroup', 20
  `MiddleNucleus', 21
  monoid, 6
  Moufang center, 21
  Moufang loop, 26
  Moufang loops, \indexit{31}
  Moufang modifications, 29
  Moufang modifications, \indexit{29}
  `MoufangLoop', 31
  multiplication group, 6
  Multiplication groups, \indexit{20}
  multiplication table, 11
  `MultiplicationGroup', 20
  `MultiplicativeNeutralElement', 16
  `MyLibraryLoop', 31
\letter N
  Naming, viewing and printing quasigroups and their elements, \indexit{9}
  `NaturalHomomorphismByNormalSubloop', 22
  neutral element, 6
  Nilpotency and central series, \indexit{22}
  `NilpotencyClassOfLoop', 22
  normal closure, 21
  normal subloop, 21
  Normal subloops, \indexit{21}
  `NormalClosure', 21
  `NormalizedQuasigroupTable', 11
  `Nuc', 21
  nuclear extension, 6
  nuclear square loop, 26
  `NuclearExtension', 14
  Nuclei, commutant, center, and associator subloop, \indexit{21}
  nucleus, 21
  `NucleusOfLoop', 21
  `NucleusOfQuasigroup', 21
\letter O
  octonion loop, 32
  octonions, 32
  `One', 16
  `Opposite', 15
  opposite quasigroup, 15
  Opposite quasigroups and loops, \indexit{15}
  Osborn loop, 28
\letter P
  Paige loop, 33
  Paige loops, \indexit{33}
  `PaigeLoop', 33
  `Parent', 18
  Parent of a quasigroup, \indexit{18}
  `PosInParent', 18
  `Position', 18
  power alternative loop, 27
  Power alternative loops, \indexit{27}
  power-associative loop, 16, 25
  power-associativity, 17
  Powers and inverses, \indexit{17}
  principal isotopism, 6
  principal loop isotope, 6
  `PrincipalLoopIsotope', 14
  Products of loops, \indexit{15}
\letter Q
  quasigroup, 6
  quasigroup table, 11
  `QuasigroupByCayleyTable', 12
  `QuasigroupByLeftSection', 13
  `QuasigroupByRightSection', 13
  `QuasigroupFromFile', 12
  Quasigroups and loops, \indexit{6}
\letter R
  RC-loop, 26
  relative left multiplication group, 20
  relative multiplication group, 20
  relative right multiplication group, 20
  `RelativeLeftMultiplicationGroup', 20
  `RelativeMultiplicationGroup', 20
  `RelativeRightMultiplicationGroup', 20
  Representing quasigroups, \indexit{8}
  right A-loop, 28
  right alternative loop, 26
  right Bol loop, 26
  right Bruck loop, 28
  right conjugacy closed loop, 27
  right distributive quasigroup, 26
  right division, 16
  right inner mapping, 20
  right inner mapping group, 20
  right inverse, 17
  right inverse property, 25
  right multiplication group, 6
  right nuclear square loop, 26
  right nucleus, 21
  right power alternative loop, 27
  right section, 6
  right translation, 6
  `RightCosets', 19
  `RightDivision', 16
  `RightDivisionCayleyTable', 17
  `RightInnerMapping', 20
  `RightInnerMappingGroup', 20
  `RightInverse', 17
  `RightMultiplicationGroup', 20
  `RightNucleus', 21
  `RightSection', 19
  `RightTranslation', 19
  `RightTransversal', 19
\letter S
  sedenions, 33
  semigroup, 6
  semisymmetric quasigroup, 25
  `SetLoopElmName', 10
  `SetQuasigroupElmName', 10
  simple Bol loop, 13
  simple loop, 9, 21
  `Size', 16
  Small loops, \indexit{33}
  `SmallLoop', 33
  Solvability, \indexit{22}
  Some properties of quasigroups, \indexit{25}
  Steiner loop, 28
  Steiner loops, \indexit{32}
  Steiner quasigroup, 26
  `SteinerLoop', 32
  strongly nilpotent loop, 22
  `Subloop', 18
  `Subquasigroup', 18
  Subquasigroups and subloops, \indexit{18}
\letter T
  Test files, \indexit{5}
  Testing Cayley tables, \indexit{11}
  totally symmetric quasigroup, 25
  Translations, \indexit{6}
  Translations and sections, \indexit{19}
  transversal, 13, 19
  Triality for Moufang loops, \indexit{29}
  `TrialityPcGroup', 30
  `TrialityPermGroup', 30
  two-sided inverse, 6
  two-sided inverses loop, 25
\letter U
  unipotent quasigroup, 26
  upper central series, 22
  `UpperCentralSeries', 22
\letter W
  weak inverse property, 25
