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CLASSIFICATION OF NILPOTENT PRIMITIVE LINEAR GROUPS OVER FINITE FIELDS

Published online by Cambridge University Press:  11 October 2004

A. S. DETINKO  and
D. L. FLANNERY
A. S. DETINKO
Affiliation:
Department of Applied Mathematics, Polotsk State University, Novopolotsk, Belarus e-mail: detinko@yahoo.com
D. L. FLANNERY
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: dane.flannery@nuigalway.ie
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Abstract

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We present a classification of the nilpotent primitive subgroups of $\mathrm{GL}(n,q)$, up to conjugacy in $\mathrm{GL}(n,q)$. Groups in the classification are specified explicitly by generating sets of matrices, where each generating set has size at most 2. Additionally we give an algorithm designed to provide electronic access to the classification for any $n$ and $q$.

Keywords

20H30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 3 , September 2004 , pp. 585 - 594
Copyright
© 2004 Glasgow Mathematical Journal Trust