On Groups with Enough Finite Representations
نویسنده
چکیده
It has been conjectured that the group algebra Q[G] of a discrete group G over the rational numbers Q is semi-simple. In this paper we consider irreducible representations of this algebra satisfying certain finiteness conditions and see just how much information these yield towards solving the above problem. We show in fact for a finitely generated group G, Q[G] has "enough" of these representations to guarantee that it is semi-simple if and only if G is a subdirect product of finite groups. We use freely the basic results on the irreducible representations and the Jacobson radical of an algebra as found in [2].
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