Group rings of finite simple groups

Abstract

Let G be a finite non-abelian simple group. In the first part we consider the question whether CG determines G up to isomorphism. This question is closely related to a recent conjecture of B. Huppert that G is determined up to a direct abelian factor by its set of ordinary character degrees. We sketch a proof that a finite simple group is determined by a11 its group algebras over a field.