Vol. 34, No. 1, 1970

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The group character and split group algebras

George Szeto

Vol. 34 (1970), No. 1, 183–191

G. J. Janusz defined 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 projective and separable splitting ring for G. Let M be a RG-module and R0 be a subring of R. Then we say that M is realizable in R0 if and only if there exists a R0G-module N such that MR R0N as left RG-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.

Mathematical Subject Classification
Primary: 20.80
Received: 18 August 1969
Published: 1 July 1970
George Szeto