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Published online by Cambridge University Press: 01 May 1997
Let G and A be finite groups with coprime orders, and suppose that A acts on G by automorphisms. Let π(G, A)[ratio ]IrrA(G)→Irr (CG(A)) be the Glauberman–Isaacs correspondence. Let B[les ]A and χ∈IrrA(G). We exhibit a counterexample to the conjecture that χπ(G, A) is an irreducible constituent of the restriction of χπ(G, B) to CG(A).