## Computing irreducible representations of supersolvable groups over small finite fields

We present an algorithm to compute a full set of irreducible representations of a supersolvable group G over a finite field K, charK |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](Gal(L/K), GL(n, L)) vanishes for all n ? 1

Published in:
Mathematics of Computation, 66, 218, 779-786
Year:
1997
Publisher:
American Mathematical Society
ISSN:
0025-5718
Keywords:
Laboratories: