Title
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Recognising tensor-induced matrix groups  

Authors
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C.R. Leedham-Green 
Queen Mary & Westfield College, University of London

E.A. O'Brien 
University of Auckland 

Abstract
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We present an algorithm to decide whether or
not a matrix group defined over a finite field is \ti.

More precisely, let $G$ be a 
subgroup of $\GL(d, F)$, where $F = \GF(q)$ and $q = p^e$
for some prime $p$, and let $V$ be the natural $FG$-module.
We assume that $d$ has a proper factorisation as $u^r$
and seek to answer the following question: 
does $G$ preserve a decomposition of $V$ as
$$U_1 \otimes U_2 \otimes \cdots \otimes U_r$$
where each $U_i$ has dimension $u > 1$ and $r > 1$,
and the set of $U_i$ is permuted by $G$?


Preprint September 2000