On the Characters of Soluble Groups

Abstract

The theory of representations of finite groups, which was originated by G. Frobenius, has been developed by I. Schur to become popular and studied more and more profoundly by R. Brauer even in the current stage of modern algebra. However, it seems that its applications to the structure theory of finite groups are still far from being satisfactory, partially because these two theories for structure and for representation are not firmly tied up.