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Primitivity testing of finite nilpotent linear groups

Part of: Other groups of matrices Representation theory of groups

Published online by Cambridge University Press:  01 March 2011

Tobias Rossmann
Tobias Rossmann*
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland (email: tobias.rossmann@googlemail.com)

Abstract

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We describe a practical algorithm for primitivity testing of finite nilpotent linear groups over various fields of characteristic zero, including number fields and rational function fields over number fields. For an imprimitive group, a system of imprimitivity can be constructed. An implementation of the algorithm in Magma is publicly available.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 20H20: Other matrix groups over fields
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 87 - 98
Copyright
Copyright © London Mathematical Society 2011

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