Acta Scientiarum Naturalium Universitatis Pekinensis

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

REN Guoqiang   

  1. Mathamatical Office, Metallugical Branch College of Tianjin University, Tianjin, 300400
  • Received:1994-10-24 Online:1995-01-20 Published:1995-01-20



  1. 天津大学冶金分校基础部, 天津,300400

Abstract: In this note, we obtain the following main result. Theorem A: Suppose and let B and b are blocks of RG and RH respectively, and their block idempotents are eB and eb 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)eB·eb=eb; (4)for any X∈Irr(b), all the irreducible constituents of XG belong to B.

Key words: Brauer Correspondenee, pblock, idempotents, defect group

摘要: 在这篇文章中,我们得到了下列主要结果:定理A设分别是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)eBeb=eb;(4)任给X∈Irr(b),则X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

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