Morita Equivalent Blocks in Subgroups of Finite Groups  

作　　者：YANG Qinqin FAN Yun 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China [2]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2006年第3期469-472,共4页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Programfor the BasicScience Researches of China(G19990751)

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.

关 键 词：naturally Morita equivalence G-ALGEBRA defect pointed group source algebra 

分 类 号：O152.6[理学—数学]