Torsion-free endotrivial modules

被引：6

作者：

Carlson, Jon F. ^{[1
]}

Mazza, Nadia ^{[2
]}

Thevenaz, Jacques ^{[3
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

[3] Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland

来源：

JOURNAL OF ALGEBRA | 2014年 / 398卷

基金：

美国国家科学基金会;

关键词：

Modular representations of finite groups; ENDO-PERMUTATION MODULES; TRIVIAL MODULES; CLASSIFICATION;

D O I：

10.1016/j.jalgebra.2013.01.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and let T(G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We investigate the torsion-free part TF(G) of the group T(G) and look for generators of TF(G). We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more precise results in some specific cases. We also conjecture that TF(G) can be generated by modules belonging to the principal block and we prove the conjecture in some cases. (C) 2013 Published by Elsevier Inc.

引用

页码：413 / 433

页数：21

共 19 条

[1] A construction of endo-permutation modules [J].