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# GAP 4 Package recog

## Group Recognition Methods

1.0

November 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, 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

Peter Brooksbank

Frank Celler

Stephen Howe

Maska Law

Stephen Linton

Gunter Malle

Eamonn O'Brien

Colva Roney-Dougal

### 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 recog-Package
3 Methods for recognition
3.1 Methods for permutation groups
3.1-1 `TrivialPermGroup`
3.1-2 `ThrowAwayFixedPoints`
3.1-3 `Pcgs`
3.1-4 `VeryFewPoints`
3.1-5 `Nontransitive`
3.1-6 `Giant`
3.1-7 `Imprimitive`
3.1-8 `SnkSetswrSr`
3.1-9 `StabChain`
3.2 Methods for matrix groups
3.2-1 `TrivialMatrixGroup`
3.2-2 `DiagonalMatrices`
3.2-3 `ReducibleIso`
3.2-4 `BlockLowerTriangular`
3.2-5 `BlockDiagonal`
3.2-6 `GoProjective`
3.2-7 `BlockScalar`
3.2-8 `LowerLeftPGroup`
3.3 Methods for projective groups
3.3-1 `TrivialProjectiveGroup`
3.3-2 `ProjDeterminant`
3.3-3 `ReducibleIso`
3.3-4 `BlocksModScalars`
3.3-5 `NotAbsolutelyIrred`
3.3-6 `Subfield`
3.3-7 `Derived`
3.3-8 `LowIndex`
3.3-9 `C6`
3.3-10 `Tensor`
3.3-11 `TwoLargeElOrders`
3.3-12 `StabilizerChain`
3.3-13 `BlockScalarProj`
3.4 Methods for black box groups
4 Examples
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