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XMod

Crossed Modules and Cat1-Groups

2.69

20 July 2018

Christopher D. Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: http://pages.bangor.ac.uk/~mas023/
Address:
Dr. C.D. Wensley
School of Computer Science
Bangor University
Dean Street
Bangor
Gwynedd LL57 1UT
UK

Murat Alp
Email: muratalp@nigde.edu.tr
Address:
Prof. Dr. M. Alp
Ömer Halisdemir University
Art and Science Faculty
Mathematics Department
Nigde
Turkey

Alper Odabas
Email: aodabas@ogu.edu.tr
Address:
Dr. A. Odabas
Osmangazi University
Arts and Sciences Faculty
Department of Mathematics and Computer Science
Eskisehir
Turkey

Enver Onder Uslu

Abstract

The XMod package provides functions for computation with

XMod was originally implemented in 1996 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].

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

© 1996-2018, Chris Wensley et al.

The XMod package 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 [LN17] and AutoDoc [GH17] packages.

The procedure used to produce new releases uses the package GitHubPagesForGAP [Hor17] and the package ReleaseTools.

Contents

1 Introduction
2 2d-groups : crossed modules and cat1-groups
3 2d-mappings
4 Isoclinism of groups and crossed modules
5 Whitehead group of a crossed module
6 Actors of 2d-groups
7 Induced constructions
8 3d-groups and 3d-mappings : crossed squares and cat^2-groups
9 Crossed modules of groupoids
10 Applications
11 Utility functions
12 Development history
References
Index

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