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recog

A package for constructive recognition of permutation and matrix groups

1.5.1

19 May 2026

Max Neunhöffer
Email: max@9hoeffer.de

Ákos Seress

Copyright

© 2005-2014 by Max Neunhöffer and Ákos Seress

© 2005-2026 by its authors, see file COPYRIGHT for details.

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or (at your option) any later version.

Contents

1.1 Overview over this manual

1.2 Feedback and support

1.3 Literature (selection)

2 Installation of the recog package

3 Recog package for user

3.1 Theoretical background

  3.2-1 RecogniseGroup
  3.2-2 RecognisePermGroup
  3.2-3 RecogniseMatrixGroup
  3.2-4 RecogniseProjectiveGroup

3.4 Possible applications

  3.4-1 Size
  3.4-2 \in
  3.4-3 SLPforNiceGens
  3.4-4 DisplayCompositionFactors

4 Group recognition

4.1 The recursive procedure

4.1-1 RecogniseGeneric
4.1-2 TryFindHomMethod

4.2 Recognition nodes

  4.2-1 RecogNodeFamily
  4.2-2 IsRecogNode
  4.2-3 RecogNode
  4.2-4 IsLeaf
  4.2-5 IsReady
  4.2-6 Grp
  4.2-7 Homom
  4.2-8 NiceGens
  4.2-9 pregensfac
  4.2-10 ImageRecogNode
  4.2-11 KernelRecogNode
  4.2-12 ParentRecogNode
  4.2-13 fhmethsel
  4.2-14 slpforelement
  4.2-15 SLPforElement
  4.2-16 StdPresentation
  4.2-17 IsCorrect
  4.2-18 methodsforimage
  4.2-19 validatehomominput
  4.2-20 ValidateHomomInput
  4.2-21 calcnicegens
  4.2-22 CalcNiceGensGeneric
  4.2-23 CalcNiceGensHomNode
  4.2-24 CalcNiceGens
  4.2-25 slptonice
  4.2-26 CalcStdPresentation
  4.2-27 gensN
  4.2-28 findgensNmeth
  4.2-29 FindKernelRandom
  4.2-30 FindKernelDoNothing
  4.2-31 FindKernelFastNormalClosure
  4.2-32 gensNslp
  4.2-33 immediateverification
  4.2-34 isone
  4.2-35 isequal
  4.2-36 OrderFunc
  4.2-37 Other components of recognition nodes

4.3 Methods to find homomorphisms

4.3-1 FindHomomorphism
4.3-2 SLPforElementGeneric

6 Methods for recognition

6.1 Methods for generic groups

  6.1-1 FewGensAbelian
  6.1-2 KnownNilpotent
  6.1-3 SnAnUnknownDegree
  6.1-4 TrivialGroup

6.2 Methods for permutation groups

  6.2-1 BalTreeForBlocks
  6.2-2 Giant
  6.2-3 Imprimitive
  6.2-4 LargeBasePrimitive
  6.2-5 MovesOnlySmallPoints
  6.2-6 NonTransitive
  6.2-7 Pcgs
  6.2-8 PcgsForBlocks
  6.2-9 StabChain
  6.2-10 StabilizerChainPerm
  6.2-11 ThrowAwayFixedPoints

6.3 Methods for matrix groups

  6.3-1 BlockDiagonal
  6.3-2 BlockLowerTriangular
  6.3-3 BlockScalar
  6.3-4 DiagonalMatrices
  6.3-5 GoProjective
  6.3-6 KnownStabilizerChain
  6.3-7 LowerLeftPGroup
  6.3-8 NaturalSL
  6.3-9 ReducibleIso
  6.3-10 Scalar

6.5 Unused methods

7 Miscellaneous

7.1 Naming of groups

7.1-1 RecogniseClassical
7.1-2 DisplayRecog

7.2 Renaming of recog functions and operations

8 How to write a recognition method

8.1 Leaf methods

8.2 Elements with memory

8.3 Splitting methods

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