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# GAP 4 Package genss

## generic Schreier-Sims

1.3

September 2009

Max Neunhöffer
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 University of St Andrews North Haugh St Andrews, Fife KY16 9SS Scotland, UK

Felix Noeske
Email: felix.noeske@math.rwth-aachen.de
Homepage: http://www.math.rwth-aachen.de/~Felix.Noeske
Address:
Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany

### Copyright

© 2006-2009 by Max Neunhöffer and Felix Noeske

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or higher.

### Contents

1 Introduction
1.1 Philosophy
1.2 Overview over this manual
2 Installation of the genss-Package
3 Stabiliser Chains
3.1 Computing stabiliser chains
3.1-1 StabilizerChain
3.2 Options for the computation of stabiliser chains
3.2-1 GENSS_IsOneProjective
3.3 How base points are chosen
3.3-1 FindBasePointCandidates
3.4 Using stabiliser chains
3.4-1 SiftGroupElement
3.4-2 SiftGroupElementSLP
3.4-3 StrongGenerators
3.4-4 NrStrongGenerators
3.4-5 BaseStabilizerChain
3.4-6 Size
3.4-7 Random
3.4-8 \in
3.4-9 IsProved
3.4-10 GroupIteratorByStabilizerChain
3.4-11 SetStabilizerChain
3.4-12 StoredStabilizerChain
3.4-13 StabChainOp
3.4-14 SiftBaseImage
3.4-15 SLPChainStabilizerChain
3.4-16 GroupHomomorphismByImagesNCStabilizerChain
3.4-17 FindShortGeneratorsOfSubgroup
3.4-18 Stab
4 Backtrack search methods
4.1 Setwise stabilisers
4.1-1 SetwiseStabilizer
4.1-2 SetwiseStabilizerPartitionBacktrack
4.2 Generic backtrack search
4.2-1 BacktrackSearchStabilizerChainElement
4.2-2 BacktrackSearchStabilizerChainSubgroup
5 Examples
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