Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup

被引:3
|
作者
Koshitani, Shigeo [1 ]
Lassueur, Caroline [2 ]
机构
[1] Chiba Univ, Grad Sch Sci, Dept Math, Inage Ku, 1-33 Yayoi Cho, Chiba 2638522, Japan
[2] TU Kaiserslautern, FB Math, Postfach 3049, D-67653 Kaiserslautern, Germany
基金
瑞士国家科学基金会;
关键词
ENDOTRIVIAL MODULES;
D O I
10.1515/jgth-2015-0044
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We provide a description of the torsion subgroup TT(G) of the finitely generated abelian group T(G) of endo-trivial kG-modules in the case that G has a dihedral Sylow 2-subgroup of order at least 8 and k is an algebraically closed field of characteristic p = 2. Specifically, we prove that TT(G) congruent to X(G), the group of one-dimensional kG-modules, except possibly when G/O2'(G) congruent to u(6), the alternating group of degree 6; in which case G may have nine-dimensional simple torsion endo-trivial modules. Our results complement the tame-representation type investigation of endo-trivial modules started by Carlson-Mazza-Thevenaz in the cases of semi-dihedral and generalized quaternion Sylow 2-subgroups. Furthermore, we provide a general reduction result, valid at any prime p, to recover the structure of TT(G) from the structure of TT(G/H), where H is a normal p'-subgroup of G.
引用
收藏
页码:635 / 660
页数:26
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