Endomorphism rings of permutation modules

JOURNAL OF ALGEBRA

卷:324

Article

Naehrig, Natalie

关键词: Alperin's weight conjecture;    Permutation modules;    Endomorphism ring of permutation modules;    Cartan matrix;   

DOI  :  10.1016/j.jalgebra.2009.12.011

来源: Elsevier

【 摘 要 】

Let k be an algebraically closed field of characteristic p and G a finite group. Then the permutation module k(p)(G) of G on the cosets of a Sylow p-subgroup P is via Fitting correspondence strongly related to its endomorphism ring End(kG) (k(p)(G)). On the other hand, each Green correspondent in G of a weight module of G occurs as a direct summand of k(p)(G). This fact suggests to analyze both structures, the permutation module and the associated endomorphism ring towards hints at a proof for Alperin's weight conjecture. We present a selection of such investigations for different groups and characteristics. In particular we focus on the socle and head constituents of the indecomposable direct summands of k(p)(G) and of the PIMs of C(C). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free