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A Constructive Brauer-Witt Theorem for Certain Solvable Groups

Published online by Cambridge University Press:  20 November 2018

Allen Herman
Allen Herman*
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, S4S 0A2 e-mail: aherman@math. uregina. ca
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Abstract

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Division algebras occurring in simple components of group algebras of finite groups over algebraic number fields are studied. First, well-known restrictions are presented for the structure of a group that arises once no further Clifford Theory reductions are possible. For groups with these properties, a character-theoretic condition is given that forces the p-part of the division algebra part of this simple component to be generated by a predetermined p-quasi-elementary subgroup of the group, for any prime integer p. This is effectively a constructive Brauer-Witt Theorem for groups satisfying this condition. It is then shown that it is possible to constructively compute the Schur index of a simple component of the group algebra of a finite nilpotent-by-abelian group using the above reduction and an algorithm for computing Schur indices of simple algebras generated by finite metabelian groups.

Keywords

20C1516S34
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1196 - 1209
Copyright
Copyright © Canadian Mathematical Society 1996

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