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# recog

## A collection of group recognition methods

1.2.5

08/03/2016

Max Neunhöffer
Email: max@9hoeffer.de
Homepage: http://www-groups.mcs.st-and.ac.uk/~neunhoef
Address:
Gustav-Freytag-Straße 40
50354 Hürth
Germany

Ákos Seress

Nurullah Ankaralioglu
Email: ankarali@atauni.edu.tr

Peter Brooksbank
Email: pbrooksb@bucknell.edu
Homepage: http://www.facstaff.bucknell.edu/pbrooksb/
Address:
Peter A. Brooksbank
Mathematics Department
Bucknell University
Lewisburg, PA 17837
USA

Frank Celler
Email: frank@celler.de
Homepage: http://www.celler.de/

Stephen Howe
Address:
Unknown

Maska Law
Email: maska@maths.uwa.edu.au
Address:
Maska Law
University of Western Australia
School of Mathematics and Statistics
35 Stirling Highway
Crawley 6009
Western Australia

Steve Linton
Email: sal@cs.st-andrews.ac.uk
Homepage: http://www-circa.mcs.st-and.ac.uk/~sal/
Address:
School of Computer Science
Jack Cole Building
North Haugh
St Andrews, Fife KY16 9SX
Scotland, UK

Gunter Malle
Email: malle@mathematik.uni-kl.de
Homepage: http://www.mathematik.uni-kl.de/~malle/

Alice Niemeyer
Email: alice@maths.uwa.edu.au
Homepage: http://www.maths.uwa.edu.au/~alice/
Address:
Alice C. Niemeyer
University of Western Australia
School of Mathematics and Statistics
35 Stirling Highway
Crawley 6009
Western Australia

Eamonn O'Brien
Email: obrien@math.auckland.ac.nz
Homepage: http://www.math.auckland.ac.nz/~obrien/

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

Max Horn
Email: max.horn@math.uni-giessen.de
Homepage: http://www.quendi.de/math
Address:
AG Algebra
Mathematisches Institut
Justus-Liebig-Universität Gießen
Arndtstraße 2
35392 Gießen
Germany

### Copyright

© 2005-2014 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
1.3 Feedback
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 `KnownStabilizerChain`
3.2-3 `DiagonalMatrices`
3.2-4 `FewGensAbelian`
3.2-5 `ReducibleIso`
3.2-6 `BlockLowerTriangular`
3.2-7 `BlockDiagonal`
3.2-8 `GoProjective`
3.2-9 `BlockScalar`
3.2-10 `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
References
Index
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