CHARACTER CORRESPONDENCES AND SUBGROUPS OF OPERATOR GROUPS

Let A and G be finite groups with coprime orders, and suppose that A a cts on G by automorphisms. Let pi(G, A) :Irr(A)(G) --> Irr(C-G(A)) be the Glauberman-Isaacs correspondence. Let B less than or equal to A an d let chi is an element of Irr(A)(G). We examine the conjecture that c hi pi(G, A) is an irreducible constituent of the restriction of chi pi (G, B) to C-G(A) and show that ii is Valid if G is supersolvable. Then , we show when the analog of this conjecture for Brauer characters and the Uno-Wolf correspondence holds. (C) 1998 Academic Press.