LAUSR

Abstract In this paper, we introduce the notion of generalized Brauer morphism for F G -modules with respect to a p-subgroup of G. This generalization is based on p-indecomposable decompositions of F G -modules. The generalized Brauer morphism is compatible with the Brauer morphism introduced by M. Broue when applied to p-permutation modules. We generalized some well-known results of p-permutation modules through generalized Brauer morphism to arbitrary modules. In particular, we show that the vertices of an indecomposable module M are the maximal p-subgroups P such that the image of M under the generalized Brauer morphism with respect to P is nonzero and that the image is the Green correspondent of M. As an example, we also compute the generalized Brauer morphisms for indecomposable modules with cyclic vertices.