The group character and split group algebras

Abstract

a splitting ring R for a group G of order n invertible in R. Then, the Brauer splitting theorem was given by G. Szeto which proves the existence of a finitely generated protective and separable splitting ring for G. Let M be a J?G-module and R o be a subring of R. Then we say that M is realizable in R o if and only if there exists a R 0 Gmodule N such that M s R RQ N as left i?G-modules. This paper gives a characterization of splitting rings in terms of the concept of realizability as in the field case. The other main results in this paper are the structure theorem for split group algebras and some properties of group characters.