Abstract

. In the rst part of this note we present a Monte Carlo algorithm that decides if a given set of matrices generates a group containing the special linear group. In the second part we give timings and extend the algorithm to the other classical groups. 1. Introduction Inspired by the Neumann-Praeger algorithm [6] for recognising whether the subgroup of GL(d; q) generated by some nite subset contains SL(d; q), we present our own version. The two methods are both Monte Carlo algorithms, in that they will either give a positive answer with proof, or a negative answer to a prescribed degree of condence, subject to the fact that both require a number of random elements of the group, which will in fact be produced by multiplying elements of the given generating set X. Both algorithms use the Aschbacher classication of subgroups of classical groups, see [3], and hence will extend to recognising whether subsets of other classical groups generate the whole group. Our algorithm is easier to ...

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