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# GAP 4 Package recogbase

## A framework for group recognition

1.0

November 2009

Max Neunhoeffer
Email: neunhoef@mcs.st-and.ac.uk
Homepage: http://www-groups.mcs.st-and.ac.uk/~neunhoef/
Address:
School of Mathematics and Statistics, Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK

Ákos Seress
Email: akos@math.ohio-state.edu
Homepage: http://www.math.ohio-state.edu/people/display/display.php?ID=302
Address:
Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210 USA

### Copyright

© 2005-2009 by Max Neunhöffer and Ákos Seress

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 Introduction
1.1 Philosophy
1.2 Overview over this manual
2 Installation of the recogbase-Package
3 Method Selection
3.1 What are methods?
3.1-1 AddMethod
3.2 How methods are called
3.2-1 CallMethods
4 Group Recognition
4.1 The recursive procedure
4.1-1 RecogniseGeneric
4.1-2 RecognisePermGroup
4.1-3 RecogniseMatrixGroup
4.1-4 RecogniseProjectiveGroup
4.1-5 RecogniseBBGroup
4.1-6 RecogniseGroup
4.1-7 FindHomDbPerm
4.1-8 FindHomMethodsPerm
4.1-9 SLPforElementFuncsPerm
4.1-10 FindHomDbMatrix
4.1-11 FindHomMethodsMatrix
4.1-12 SLPforElementFuncsMatrix
4.1-13 FindHomDbProjective
4.1-14 FindHomMethodsProjective
4.1-15 SLPforElementFuncsProjective
4.1-16 FindHomDbBB
4.1-17 FindHomMethodsBB
4.1-18 SLPforElementFuncsBB
4.2 Recognition info records
4.2-1 RecognitionInfoFamily
4.2-2 IsRecognitionInfo
4.2-3 IsLeaf
4.2-4 IsReady
4.2-5 Grp
4.2-6 Homom
4.2-7 NiceGens
4.2-8 pregensfac
4.2-9 RIFac
4.2-10 RIKer
4.2-11 RIParent
4.2-12 fhmethsel
4.2-13 slpforelement
4.2-14 SLPforElement
4.2-15 StdPresentation
4.2-16 methodsforfactor
4.2-17 calcnicegens
4.2-18 CalcNiceGensGeneric
4.2-19 CalcNiceGensHomNode
4.2-20 CalcNiceGens
4.2-21 slptonice
4.2-22 gensN
4.2-23 findgensNmeth
4.2-24 FindKernelRandom
4.2-25 FindKernelDoNothing
4.2-26 FindKernelFastNormalClosure
4.2-27 gensNslp
4.2-28 immediateverification
4.2-29 forkernel
4.2-30 forfactor
4.2-31 isone
4.2-32 isequal
4.2-33 Other components of recognition info records
4.3 Methods to find homomorphisms
4.3-1 FindHomomorphism
4.3-2 SLPforElementGeneric
4.4 Conventions for the recognition of permutation groups
4.5 Conventions for the recognition of matrix groups
4.6 Conventions for the recognition of projective groups
4.7 Conventions for the recognition of black box groups
5 After successful recognition
5.1 Functions and methods for recognition info records
5.1-1 SLPforNiceGens
5.1-2 \in
5.1-3 Size
5.1-4 DisplayCompositionFactors
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