A Generalized Brauer Induction Theorem and Its Converse

Abstract

Let G be a finite group, S a unitary subring of the complex number field ℂ and R(G) the character ring of G. Let π be the set of rational prime numbers whose inverses do not belong to S. Denote the family of all p-elementary subgroups of G by W(π), where p runs over π. It is proved that, in the sense of conjugation, W(π) is the least family [Formula: see text] of subgroups of G such that the S-linear map [Formula: see text] is surjective.