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Groupoids, graphs of groups, and graphs of groupoids

Version 1.46


Emma Moore

Chris Wensley
School of Computer Science, Bangor University,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.


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. The most basic structure introduced is that of magma with objects, followed by semigroup with objects, then monoid with objects and finally groupoid which is a group with objects.

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. Version 1.15 came out with the first release of GAP 4.5 in June 2012, and was submitted for official acceptance as a GAP package. Gpd became an accepted GAP package in May 2015. The latest version is 1.46 of 21st February 2017, prepared for GAP 4.8.

Recent versions implement many of the constructions described in the paper [AW10] for automorphisms of groupoids.

Bug reports, suggestions and comments are, of course, welcome. Please submit an issue at or send an email to the last author at


© 2000-2017 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.


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.


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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