The Glauberman Correspondence and Subgroups of Operator Groups: a Counterexample

Let G and A be finite groups with coprime orders, and supposethat A acts on G by automorphisms. Let (G, A):Irr_A(G)Irr(C_G(A))be the Glauberman–Isaacs correspondence. Let B A andIrr_A(G). We exhibit a counterexample to the conjecture that(G, A) is an irreducible constituent of the restriction of (G,B) to C_G(A). 1991 Mathematics Subject Classification 20C15.