Blocks of Endomorphism Algebras Original Research Article

Let imageG be a p-modular group algebra, let H be a subgroup of G containing the normaliser of a p-subgroup P, let A be an imageG-module, and B an imageH-module. After defining defect groups of blocks of EndimageG(A) and of EndimageH(B), we associate a certain block of End(imageH)(A ↓ H) with each block of EndimageG(A) having defect group P. Similarly, we associate a certain block of EndimageG(B ↑ G) with each block of EndimageH(B) with defect group P. These associations are compatible with the correspondences of Brauer and of Green, and, in particular, they partly generalise Brauer′s First and Second Main Theorems. The theory simplifies when working within blocks of group algebras with abelian defect groups.