On semi-simple group algebras. I
Eugene Spiegel, Peter Trojan · Pacific Journal of Mathematics · 1975
For F a field and G a group, let FG denote the group algebra of G over F. Let ^ be a class of finite groups, and ^ a class of fields.Call the fields F ± and F 2 {F t e^i = 1, 2) equivalent on S? if for all G, He &, FiGczFtH if and only if F 2 G~F 2 H.In this note we begin a study of this equivalence relation, taking the case where ^ consists of all finite p-groups and ^~ those fields F, for which FG is simi-simple for all Ge Sf.