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### 5. The Modular Isomorphism Problem

#### 5.1 Known results on MIP

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#### 5.2 Invariants determined by group algebras

##### 5.2-1 SandlingFactorGroup

`> SandlingFactorGroup`( G ) | ( attribute )

Returns: factorgroup

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##### 5.2-2 JenningsFactors

`> JenningsFactors`( G ) | ( attribute )

Returns: list of lists of IdGroup

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##### 5.2-3 NumberOfConjugacyClassesPPowers

`> NumberOfConjugacyClassesPPowers`( G ) | ( attribute )

Returns: list of integers

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##### 5.2-4 ClassSumNumbers

`> ClassSumNumbers`( G ) | ( attribute )

Returns: list of integers

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##### 5.2-5 QuillenSeries

`> QuillenSeries`( G ) | ( attribute )

Returns: list of integers

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##### 5.2-6 RoggenkampParameter

`> RoggenkampParameter`( G ) | ( attribute )

Returns: integer

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##### 5.2-7 RoggenkampParameterForNormalSubset

`> RoggenkampParameterForNormalSubset`( G, S ) | ( function )

Returns: integer

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##### 5.2-8 KernelSize

`> KernelSize`( FG[, n, m, k] ) | ( attribute )

Returns: integer or fail

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#### 5.3 MIP testing tools

##### 5.3-1 PrintMIPInvariants

`> PrintMIPInvariants`( G ) | ( function )

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##### 5.3-2 PrintMIPInvariantsTable

`> PrintMIPInvariantsTable`( list, filename ) | ( function )

Returns: text file generated in the current directory

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##### 5.3-3 MIPInvariantsRecord

`> MIPInvariantsRecord`( G ) | ( function )

Returns: record

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##### 5.3-4 MIPInvariantsLibrary

`> MIPInvariantsLibrary`( n ) | ( function )

Returns: text file generated in the current directory

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##### 5.3-5 MIPInvariantsLibraryClassification

`> MIPInvariantsLibraryClassification`( invlib, mode ) | ( function )

Returns: list of lists and (optionally) a text file generated in the current directory

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##### 5.3-6 KernelSizeTest

`> KernelSizeTest`( FG, FH ) | ( function )

Returns: a list of parameters and kernel sizes or fail

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##### 5.3-7 JenningsLieAlgebraTest

`> JenningsLieAlgebraTest`( FG, FH ) | ( function )

Returns: true or false

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##### 5.3-8 MIPSplittingByKernelSize

`> MIPSplittingByKernelSize`( list, no, mode ) | ( function )

Returns: text file generated in the current directory

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##### 5.3-9 MIPSplittingByJenningsLieAlgebra

`> MIPSplittingByJenningsLieAlgebra`( list, no, mode ) | ( function )

Returns: text file generated in the current directory

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##### 5.3-10 MIPSplittingReport

`> MIPSplittingReport`( list ) | ( function )

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