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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
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

Type
Research Article
Copyright
© 2004 Glasgow Mathematical Journal Trust