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Gpd

Groupoids, graphs of groups, and graphs of groupoids

Version 1.12

21/09/2011

Emma Moore
Email: emmajmoore@yahoo.co.uk

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

Abstract

The Gpd package for GAP4 provides functions for the computation with groupoids (categories with every arrow invertible) and their morphisms; for graphs of groups, and graphs of groupoids.

It provides normal forms for Free Products with Amalgamation and for HNN-extensions when the initial groups have rewrite systems and the subgroups have finite index.

The Gpd package was originally implemented in 2000 (as GraphGpd) when the first author was studying for a Ph.D. in Bangor.

Version 1.07 was released in July 2011, to be tested with GAP 4.5 prior to its expected release in October 2011. The aim is that this version should be submitted for official acceptance as a GAP package. The latest version is 1.12.

The package now includes the more basic structure of magma with objects. It has been released to coincide with the publication of [AW10]. This version does not implement all the constructions introduced in the paper, so a new version will be released as soon as possible.

Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at c.d.wensley@bangor.ac.uk.

Copyright

© 2000-2011 Emma Moore and Chris Wensley

gpd 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 of Frank Lübeck and Max Neunhöffer.

Contents

1 Introduction
2 Many-object structures
3 Homomorphisms of many-object structures
4 Groupoids
5 Homomorphisms of Groupoids
6 Graphs of Groups and Groupoids
7 Technical Notes
8 Development History

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