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XMod

Crossed modules and cat1-groups in GAP

Version 2.59

21/03/2017

Chris Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: http://pages.bangor.ac.uk/~mas023/
Address:
School of Computer Science, Bangor University,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.

Murat Alp
Email: muratalp@nigde.edu.tr
Address:
Nigde Üniversitesi,
Fen Edebiyat Fakültesi, Matematik Bölümü
Nigde, Turkey.

Alper Odabaş
Email: aodabas@ogu.edu.tr
Homepage: http://fef.ogu.edu.tr/matbil/aodabas/
Address:
Department of Mathematics and Computer Science,
Osmangazi University, Eskişehir, Turkey

Enver Önder Uslu
Email: enveruslu@ogu.edu.tr
Homepage: http://fef.ogu.edu.tr/matbil/enveruslu/
Address:
Department of Mathematics and Computer Science,
Osmangazi University, Eskişehir, Turkey

Abstract

The XMod package provides functions for computation with

XMod was originally implemented in 1997 using the GAP3 language, when the second author was studying for a Ph.D. [Alp97] in Bangor.

In April 2002 the first and third parts were converted to GAP4, the pre-structures were added, and version 2.001 was released. The final two parts, covering derivations, sections and actors, were included in the January 2004 release 2.002 for GAP 4.4.

In October 2015 functions for computing isoclinism classes of crossed modules, written by Alper Odabaş and Enver Uslu, were added. These are contained in Chapter 4, and are described in detail in the paper [IOU16].

The current version is 2.59, released 21st March 2017 for GAP 4.8.

Bug reports, suggestions and comments are, of course, welcome. Please submit an issue at http://github.com/gap-packages/xmod/issues/ or send an email to the first author at c.d.wensley@bangor.ac.uk.

Copyright

© 1997-2017 Chris Wensley et al. XMod is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Acknowledgements

This documentation was prepared with the GAPDoc package [LN12] of Frank Lübeck and Max Neunhöffer.

The procedure used to mount new releases on GitHub uses the packages GitHubPagesForGAP [Hor14] and ReleaseTools of Max Horn.

The second author wishes to acknowledge support from Dumlupinar University and the Turkish government.

Contents

1 Introduction
2 2d-groups : crossed modules and cat1-groups
3 2d-mappings
4 Isoclinism of groups and crossed modules
5 Derivations and Sections
6 Actors of 2d-groups
7 Induced constructions
8 Crossed squares and their morphisms
9 Crossed modules of groupoids
10 Utility functions
11 Development history
References
Index

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