Computing in nilpotent matrix groups
A. S. Detinko and D. L. Flannery
Abstract: The authors of this paper present algorithms for testing
nilpotency of matrix groups over finite fields, and for deciding
irreducibility and primitivity of nilpotent matrix groups. The
algorithms also construct modules and imprimitivity systems for
nilpotent groups. In order to justify the algorithms, proofs are
given of several structural results for nilpotent linear groups,
and computational and theoretical results for abstract nilpotent
groups, which are of independent interest.
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