On the Structure of Group Algebras, I

Abstract

With this paper we begin a study of the structure of the group algebra RG of a finite group G over the ring of algebraic integers R in an algebraic number field k. The basic question is whether non-isomorphic groups can have isomorphic algebras over R. We shall show that this is impossible if G is (a) abelian,(b) Hamiltonian,(c) one of a special class of p-groups.