This document describes a package for the GAP group theory langauge which enables computations with the equivalent notions of finite, permutation em crossed modules and em cat1-groups.
The package divides into six parts, each of which has its own introduction: item for constructing crossed modules and their morphisms in section refAbout crossed modules: About crossed modules; item for cat1-groups, their morphisms, and for converting between crossed modules and cat1-groups, in section refAbout cat1-groups: About cat1-groups; item for derivations and sections and the monoids which they form under the Whitehead multiplication, in section refAbout derivations and sections: About derivations and sections; item for actor crossed modules, actor cat1-groups and the actors squares which they form, in section refAbout actors: About actors; item for the construction of induced crossed modules and induced cat1-groups, in section refAbout induced constructions: About induced constructions; item for a collection of utility functions in section refAbout utilities: About utilities.
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These seven About... sections are collected together in a separate
LaTeX file, xmabout.tex, which forms a short introduction to the package.
The package may be obtained as a compressed file by ftp from one of
the sites with a GAP archive. After decompression, instructions
for installing the package may be found in the README file.
The following constructions are planned for the next version of the package. Firstly, although sub-crossed module functions have been included, the equivalent set of sub-cat1-groups functions is not complete. Secondly, functions for pre-crossed modules, the Peiffer subgroup of a pre-crossed module and the associated crossed modules, will be added. Group-graphs provide examples of pre-crossed modules and their implementation will require interaction with graph-theoretic functions in GAP. Crossed squares and the equivalent cat2-groups are the structures which arise as "three-dimensional groups". Examples of these are implicitly included already, namely inclusions of normal sub-crossed modules, and the inner morphism from a crossed module to its actor (section refInnerMorphism for crossed modules).
GAP 3.4.4