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On the Structure of Integral Group Rings of Sporadic Groups

Published online by Cambridge University Press:  01 February 2010

Frauke M. Bleher  and
Wolfgang Kimmerle
Frauke M. Bleher
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, U.S.A., frauke@math.upenn.edu
Wolfgang Kimmerle
Affiliation:
Mathematisches Institut B, Universität Stuttgart, Pfaffenwaldring 57, D–70550 Stuttgart, Germany, kimmerle@mathematik.uni-stuttgart.de

Abstract

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The object of this article is to examine a conjecture of Zassenhaus and certain variations of it for integral group rings of sporadic groups. We prove the ℚ-variation and the Sylow variation for all sporadic groups and their automorphism groups. The Zassenhaus conjecture is established for eighteen of the sporadic simple groups, and for all automorphism groups of sporadic simple groups G which are different from G. The proofs are given with the aid of the GAP computer algebra program by applying a computational procedure to the ordinary and modular character tables of the groups. It is also shown that the isomorphism problem of integral group rings has a positive answer for certain almost simple groups, in particular for the double covers of the symmetric groups.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 274 - 306
Copyright
Copyright © London Mathematical Society 2000

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