Integral Group Rings of Finite Groups

Abstract

The main object of this paper is to show that the existence of a particular kind of isomorphism between the integral group rings of two finite groups implies that the groups themselves are isomorphic. The proof employs certain types of linear forms which are first discussed in general. These linear forms are in some way related to the bilinear forms used by Weidmann [3] in showing that groups with isomorphic character rings have the same character table, and a shorter and, in a sense, more natural proof of this result is included here as another application of these linear forms.