Glauberman correspondence of p-blocks of finite groups

Let G and A be finite groups with coprime orders. Suppose that A is solvabl e and that it acts on G by automorphisms. Let C = C-G(A). By Irr(G) and Irr (A)(G) we denote the set of all irreducible and all A-invariant irreducible characters of G, respectively. Let D less than or equal to C be a fixed p- subgroup of G for a prime p. Using the Glauberman correspondence pi (G, A): Irr(A)(G) --> Irr(C), A. Watanabe (J. Algebra 216 (1999), 548-565) recently established a Glauber man correspondence between A-invariant p-blocks B of G with defect group D and p-blocks B-1 of C with defect group D. Let Br(B) and Br(B-1) be the Bra uer correspondents of B and B-1 in N-G(D) and N-C(D), respectively. The mai n result of this article asserts that the block algebras Br(B) and Br(B-1) are Morita equivalent. Furthermore, if G is p-solvable and D is abelian, th en the block algebras B and B-1 are Morita equivalent. (C) 2001 Academic Pr ess.