THE GLAUBERMAN CORRESPONDENCE AND SUBGROUPS OF OPERATOR GROUPS - A COUNTEREXAMPLE

Let G and A 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 t he Glauberman-Isaacs correspondence. Let B less than or equal to A and chi is an element of IrrA(G). We exhibit a counterexample to the conj ecture that chi pi(G, A) is an irreducible constituent of the restrict ion of chi pi(G, B) to C-G(A).