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Computing in Nilpotent Matrix Groups

Published online by Cambridge University Press:  01 February 2010

A.S. Detinko  and
D.L. Flannery
A.S. Detinko
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland, alla.detinko@nuigalway.ie
D.L. Flannery
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland, dane.flannery@nuigalway.ie

Abstract

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We present algorithms for testing nilpotency of matrix groups over finite fields, and for deciding irreducibility and primitivity of nilpotent matrix groups. The algorithms also construct modules and imprimitivity systems for nilpotent groups. In order to justify our algorithms, we prove several structural results for nilpotent linear groups, and computational and theoretical results for abstract nil-potent groups, which are of independent interest.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 104 - 134
Copyright
Copyright © London Mathematical Society 2006

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