UNSPECIFIED (1994) TESTING MODULES FOR IRREDUCIBILITY. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 57 (Part 1). pp. 1-16. ISSN 0263-6115

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Abstract

A practical method is described for deciding whether or not a finite-dimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalisation of the Parker-Norton 'Meataxe' algorithm, but it does not depend for its efficiency on the field being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a finite field, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
Publisher:	AUSTRALIAN MATHEMATICS PUBL ASSOC INC
ISSN:	0263-6115
Date:	August 1994
Volume:	57
Number:	Part 1
Number of Pages:	16
Page Range:	pp. 1-16
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20361

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