摘要
令R为有限交换局部环,K为其剩余类域.本文研究了R上一般线性群GLnR的Carter子群的存在性及结构.得到的结果是:若charK为奇数或K=F2,GLnR中存在唯一的Carter子群的共轭类,即Sylow-2子群的正规化子;若charK=2且|K|>2,GLnR中不含Carter子群.
Let R be a finite commutative local ring and let M denote the unique maximal ideal of R and K denote the residue field of R. In the present paper, the author studied the existence and structure of the Carter subgroups of general linear groups GL nR over R. The main result is that if char K is odd or K=F 2, there is a single conjugacy class of Carter subgroups in GL nR, namely, the normalizers of the Sylow 2-subgroups; if char K=2 and |K|>2, GL nR contains no Carter subgroups.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1998年第4期773-778,共6页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金