On Inclusion of Permutation Modules

被引：0

作者：

Li Zhong WANG ^{[1
]}

机构：

[1] School of Mathematical Sciences,Peking University

来源：

Acta Mathematica Sinica,English Series | 2013年 / 04期

基金：

中国国家自然科学基金;

关键词：

Permutaion module; Schur’s lemma; Foulkes; conjecture; double cosets;

D O I：

暂无

中图分类号：

O153.3 [环论];

学科分类号：

070104 ;

摘要：

Let H1,H2 be subgroups of a finite group G. Assume that G=∪i=1mH2yiH1=∪j=1nH1gjH1 and that y1=1,g1=1.Let Di be the set consisting of right cosets of H2 contained in H2yiH1 and let dj(j=1, . . . ,n) be the set consisting of right cosets contained in H1gjH1.We define the n×m matrix Mz(z=1, . . . ,m) whose columns and rows are indexed by Di and dj respectively and the (dk,Dl) entry is |Dzgk∩Dl|. Let M=(M1, . . . ,Mm). Assume that 1H1G and 1H2G are semisimple permutation modules of a finite group G. In this paper, by using the matrix M , we give some sufficient and necessary conditions such that 1H1G is isomorphic to a submodule of 1H2G.As an application, we prove Foulkes’ conjecture in special cases.

引用

页码：717 / 728

页数：12