Computing irreducible representations of supersolvable groups over small finite fields
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- by A. Omrani and A. Shokrollahi PDF
- Math. Comp. 66 (1997), 779-786 Request permission
Abstract:
We present an algorithm to compute a full set of irreducible representations of a supersolvable group $G$ over a finite field $K$, $\operatorname {char} K\nmid |G|$, 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 $H^{1}(\operatorname {Gal}(L/K), \operatorname {GL}(n,L))$ vanishes for all $n\ge 1$.References
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Additional Information
- A. Omrani
- Affiliation: Institut für Informatik, Römerstraße 164, 53121 Bonn, Germany
- Email: amin@cs.bonn.edu
- 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
- Email: amin@icsi.berkeley.edu
- Received by editor(s): May 23, 1995
- Received by editor(s) in revised form: November 10, 1995, and May 1, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 779-786
- MSC (1991): Primary 20C15, 11R34, 20D15, 11T99
- DOI: https://doi.org/10.1090/S0025-5718-97-00839-9
- MathSciNet review: 1408377