On semi-simple group algebras. I

Abstract

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.