Alperin－Burry意义下Brauer对应的一个结果

北京大学学报（自然科学版）

Alperin－Burry意义下Brauer对应的一个结果

任国强

天津大学冶金分校基础部, 天津，300400

收稿日期:1994-10-24 出版日期:1995-01-20 发布日期:1995-01-20

A Resuet on Brauer Correspondence in the Sense of Alperin and Burry

REN Guoqiang

Mathamatical Office, Metallugical Branch College of Tianjin University, Tianjin, 300400

Received:1994-10-24 Online:1995-01-20 Published:1995-01-20

摘要/Abstract

摘要： 在这篇文章中，我们得到了下列主要结果：定理Ａ设Ｈ≤Ｇ，Ｂ，ｂ分别是ＲＧ，ＲＨ的块，其块元分别为的方群Ｄ满足D≤Z(G)，则下列等价：（１）b^-(G)=B^-；（２）e^-_Be^-_b=e^-_b；（３）e_Be_b=e_b；（４）任给X∈Irr(b)，则Ｘ^Ｇ的所有不可约分量都属于Ｂ。

关键词: Brauer对应, p块, 幂等元, 方群

Abstract: In this note, we obtain the following main result. Theorem A: Suppose Ｈ≤Ｇ and let B and b are blocks of RG and RH respectively, and their block idempotents are e_B and e_b respectively. If a defect group of b satisfies that D≤Z(G), then the following are equivalent: (1)b^~(G)=B^~; (2)e^~_B·e^~_b=e^~_b; (3)e_B·e_b=e_b; (4)for any X∈Irr(b), all the irreducible constituents of X^G belong to B.