Glasgow Mathematical Journal



CLASSIFICATION OF NILPOTENT PRIMITIVE LINEAR GROUPS OVER FINITE FIELDS


A. S. DETINKO a1 and D. L. FLANNERY a2
a1 Department of Applied Mathematics, Polotsk State University, Novopolotsk, Belarus e-mail: detinko@yahoo.com
a2 Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: dane.flannery@nuigalway.ie

Article author query
detinko as   [Google Scholar] 
flannery dl   [Google Scholar] 
 

Abstract

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 $q$.

(Received November 28 2003)
(Accepted January 22 2004)

Maths Classification

20H30.