Vol. 59, No. 2, 1975

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On semi-simple group algebras. I

Eugene Spiegel and Allan Trojan

Vol. 59 (1975), No. 2, 549–555

For F a field and G a group, let FG denote the group algebra of G over F. Let 𝒢 be a class of finite groups, and a class of fields. Call the fields F1 and F2(Fi ∈ℱi = 1,2) equivalent on 𝒢 if for all G,H ∈𝒢,F1G F1H if and only if F2G F2H. In this note we begin a study of this equivalence relation, taking the case where 𝒢 consists of all finite p-groups and those fields F, for which FG is simi-simple for all G ∈𝒢.

Mathematical Subject Classification 2000
Primary: 20C05
Received: 4 February 1975
Revised: 23 May 1975
Published: 1 August 1975
Eugene Spiegel
Allan Trojan