Endomorphism rings of permutation modules
Endomorphism rings of permutation modules
复制标题
排列模的自同态环
DOI：
10.1016/j.jalgebra.2009.12.011
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发表时间：
2010
影响因子：
0.9
通讯作者：
Natalie Naehrig
中科院分区：
文献类型：
--
作者：
Natalie Naehrig
设k为特征为p的代数闭域，G为有限群。然后，通过拟合其自同态环EndkG（kPG）强相关的对应关系，得到Sylow P -子群P上G的置换模kpgg。另一方面，G的权重模块G中的每个Green对应都是kPG的直接求和。这一事实表明，通过分析这两个结构，排列模和相关的自同态环来暗示Alperin权猜想的证明。我们为不同的群体和特征提供了这样的调查选择。我们特别关注的是不可分解的kpga和PIMs的直接总和的社会和头部成分。
Let k be an algebraically closed field of characteristic p and G a finite group. Then the permutation module kPGof G on the cosets of a Sylow p-subgroup P is via Fitting correspondence strongly related to its endomorphism ring EndkG(kPG). On the other hand, each Green correspondent in G of a weight module of G occurs as a direct summand of kPG. 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 kPGand of the PIMs of EE.