On semi-simple group algebras. I

Eugene Spiegel and Allan Trojan

Vol. 59 (1975), No. 2, 549–555

DOI: 10.2140/pjm.1975.59.549

Abstract

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 ℱ a class of fields. Call the fields F₁ and F₂(F_i ∈ℱ_i = 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 ℱ those fields F, for which FG is simi-simple for all G ∈𝒢.

Mathematical Subject Classification 2000

Primary: 20C05

Milestones

Received: 4 February 1975

Revised: 23 May 1975

Published: 1 August 1975