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U.W. Bangor - School of Informatics - Mathematics Preprints 1997

Computational discrete algebra

97.05 : ALP, M. & WENSLEY, C.D.

Enumeration of cat1-groups of low order

Abstract:

In this paper we describe a share package XMOD of functions for computing with finite, permutation crossed modules, cat1-groups and their morphisms, written using the GAP group theory programming language. The category XMod of crossed modules is equivalent to the category Cat1 of cat1-groups and we include functions emulating the functors between these categories. The monoid of derivations of a crossed module X, and the corresponding monoid of sections of a cat1-group C, are constructed using the Whitehead multiplication. The Whitehead group of invertible derivations, together with the group of automorphisms of X are used to construct the actor crossed module of X which is the automorphism object in XMod. We include a table of the 350 isomorphism classes of cat1-structures on groups of order at most 30.

Published in:

IJAC 10 (2000) 407-424.

97.32 : ALP, M.

GAP, Crossed modules, cat1-groups

Published in:

U W Bangor PhD thesis (April 1997)

Download:

gzipped postscript of the thesis: alp.ps.gz

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