Fong Characters and Correspondences in π-Separable Groups

Abstract

Let G and S be finite groups. Suppose that S acts on G with (|G|, |S| ) = 1. If S is solvable, Glauberman showed the existence of a natural bijection from lrrs(G) = ﹛ χ ∈ Irr(G) | χs = χ for a11 s ∈ S﹜ on to Irr(C), where C = CG(S). If S is not solvable, and consequently | G| is odd, Isaacs also proved the existence of a natural bijection between the above set of characters. Finally, Wolf proved that both maps agreed when both were defined ([1], [3], [10]). As in [7], let us denote by *: Irrs(G) → Irr(C) the Glauberman-Isaacs Correspondence.