Correspondences of Characters for Relatively Prime Operator Groups

Abstract

Let G be a finite group and let A be a finite solvable operator group on G . Suppose that A and G have relatively prime orders. Let T be the fixed-point subgroup of G with respect to A . We say that A fixes a complex character ζ of G if ζ (g α ) = ζ (g) for all g ∈ G and α ϵ A. Our aim in this paper is to define a one-to-one correspondence between the irreducible characters of T and those irreducible characters of G that are fixed by A , and to prove some properties of this correspondence that were mentioned in (8).