Glauberman Correspondent Of A Block

Let G be a finite group and A be another solvable finite group acting on G. Assmue that|G|and|A|are co-prime. Let b be an A-stable block idempotent of OG with a defect group P centralized by A. Let c be the Glauberman correspondent of b (refer to [12]). If there is a p-nilpotent A-stable normal subgroup of G such thatG=H·CG(A), then there is an indecomposable O(G×CG(A))-module M having the following properties:the p-subgroup△(P)={(x,x)|x∈P} of G×CG(A) is a vertex of M, M induces a Morita equivalence between OGb and OCG(A)c, and the bijection between Irr(G, b) and Irr(CG(A), c) induced by this Morita equivalence coincides with the Glauberman correspondence from Irr(G, b) to Irr(GG(A), c), which generalize the result in [13].