摘要
Let （K, O, 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 nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer 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.
Let （K, O, 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 nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer 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.
基金
Supported by the National Programfor the BasicScience Researches of China(G19990751)
