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Computing irreducible representations of supersolvable groups over small finite fields

Authors: A. Omrani and A. Shokrollahi
Journal: Math. Comp. 66 (1997), 779-786
MSC (1991): Primary 20C15, 11R34, 20D15, 11T99
MathSciNet review: 1408377
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Abstract: We present an algorithm to compute a full set of irreducible representations of a supersolvable group $G$ over a finite field $K$, ${\text {\rm char}} K\nmid |G|$, which is not assumed to be a splitting field of $G$. The main subroutines of our algorithm are a modification of the algorithm of Baum and Clausen (Math. Comp. 63 (1994), 351-359) to obtain information on algebraically conjugate representations, and an effective version of Speiser's generalization of Hilbert's Theorem 90 stating that $H^{1}({\text {\rm Gal}}(L/K), {\text {\rm GL}}(n,L))$ vanishes for all $n\ge 1$.

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Additional Information

A. Omrani
Affiliation: Institut für Informatik, Römerstraße 164, 53121 Bonn, Germany

A. Shokrollahi
Affiliation: Institut für Informatik, Römerstraße 164, 53121 Bonn, Germany
Address at time of publication: International Computer Science Institute, 1947 Center Street, Berkeley, California 94704–1198

Keywords: Computational representation theory, Galois cohomology, $p$-groups, finite fields.
Received by editor(s): May 23, 1995
Received by editor(s) in revised form: November 10, 1995, and May 1, 1996
Article copyright: © Copyright 1997 American Mathematical Society