Morita Equivalent Blocks in Subgroups of Finite Groups

摘要

Let (K, sigma, k) be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are naturally Morita equivalent of degree n if and only if A=B...B as right R[H x H]-modules and A and B have the same defect (where R {k, sigma}), which is a generalization of the result of Kulshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.