A Proof of Brauer’s Theorem on Generalized Decomposition Numbers

Abstract

In [3] R. Brauer gave a proof of his theorem on generalized decomposition numbers which was first announced in [1], and a simplification of it has been made by K. Iizuka [5]. In this note we shall show that the theorem may be proved from another point of view by using some results obtained by J. A. Green in [4].After stating some results by Green and Osima in the first and second sections we first prove a theorem on characters (Theorem 1) and by using the theorem we prove Brauer’s theorem in the fourth section.