A new GAP share package written by Chris Wensley and Murat Alp, for
calculating in crossed modules and cat1 groups is now available, and can
be collected from the GAP incoming directory in the file xmod131.tar.gz.
The GAP web page description is included below.

Derek Holt.

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XMod

Authors: Chris Wensley, Murat Alp
Language: GAP
Operating System: Any
Available from: http://www.math.rwth-aachen.de/ftp/pub/incoming/xmod131.tar.gz,

Description

This package enables construction of and computation with objects within the
equivalent categories of crossed modules and cat1-groups, where the groups
involved are finite of moderately small order.

A crossed module consists of two groups S and R, together with a homomorphism
from S to R which essentially commutes with conjugation within S and R.
Functions are provided for each of the standard constructions of crossed
modules, and for computing with sub- and quotient-structures and
homomorphisms.

A cat1-group consists of a group G together with two homomorphisms from G to G
satisfying certain conditions. It was shown by Loday that there is a natural
one-one correspondence between cat1-groups and crossed modules.

An important notion is a derivation of a crossed module, which is a map from R
to S satisfying certain conditions. It is possible to compute all (or all
regular) derivations of a crossed module. There are also functions for
computing the actor of a crossed module X, which is a crossed module whose
range is the automorphism group of X.

Authors

Chris Wensley and Murat Alp

School of Mathematics
University of Wales, Bangor
Gwynedd, LL57 1UT
GB

email: c.d.wensley@bangor.ac.uk ~e