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Complex group algebras of finite groups: Brauer's Problem 1

Author: Alexander Moretó
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 34-39
MSC (1991): Primary 20C15
Published electronically: May 10, 2005
MathSciNet review: 2150942
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Abstract: Brauer's Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number $m$ of isomorphic summands, then its dimension is bounded in terms of $m$. We prove that this is true for every finite group if it is true for the symmetric groups.

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Alexander Moretó
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, SPAIN

Received by editor(s): October 12, 2004
Published electronically: May 10, 2005
Additional Notes: Research supported by the Basque Government, the Spanish Ministerio de Ciencia y Tecnología, grant BFM2001-0180, and the FEDER
Communicated by: David J. Benson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.