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This is a page on GAP 3, which is still available, but no longer supported. The present version is GAP 4  (See  Status of GAP 3).

GAP 3 Package "smash"

The former package Smash

The package "smash" had already been superseded by the GAP 3 share package "matrix" and hence has not been transferred to GAP 4. The Smash functionality is (mostly) available as part of the GAP 4 library.

Authors

Derek F. Holt, Charles R. Leedham-Green, Eamonn O'Brien, and Sarah Rees.

Implementation

Language: GAP 3
Operating system: Any
Current version: Obsolete (in the 3.4.4 distribution)

Description

This share library provides functions which may be used to construct and investigate the structure of matrix groups defined over finite fields. These functions permit the user to construct certain types of matrix groups and G-modules; to test whether a G-module is irreducible or absolutely irreducible; to decide whether a group has certain decomposition with respect to a normal subgroup; and to select random elements with certain properties.

The code was developed as part of the on-going project to "recognise" the Aschbacher categories of matrix groups defined over finite fields.

Contact addresses

Derek F. Holt
Mathematics Institute
University of Warwick
Warwick, Coventry, CV4 7AL
UK
email: dfh@maths.warwick.ac.uk

Charles R. Leedham-Green
School of Mathematical Sciences
Queen Mary, University of London
London, E1 4NS
UK

Eamonn O'Brien
Department of Mathematics
University of Auckland
Auckland, Private Bag 92019
New Zealand
email: obrien@math.auckland.ac.nz

Sarah Rees
Department of Mathematics
University of Newcastle
Newcastle, NE1 7RU
UK
email: Sarah.Rees@ncl.ac.uk

Bibliography

The interested reader is referred to the following paper for details of the algorithms used.

[HR94] Derek F. Holt and Sarah Rees, Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57, 1994.

[HLO96a] Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien and Sarah Rees, Computing matrix group decompositions with respect to a normal subgroup, J. Algebra, 184 (3), 818-838, 1996.

[HLO96b] Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien and Sarah Rees, Testing Matrix Groups for Primitivity, J. Algebra, 184 (3), 795-817, 1996.