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| 局部环上辛群的一类极大子群 |
| A Type of Maximal Subgroups of Symplectic Groups over Local Rings |
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| DOI：10.3969/j.issn.1671-5322.2009.02.003 |
| 中文关键词: 局部环 辛群 极大子群 |
| 英文关键词: local ring symplectic group maximal subgroup |
| 基金项目: |
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| 中文摘要: |
| 典型群理论是群理论的重要组成部分,辛群是-类重要的典型群.典型群的子群结构研究的目的是定出所有典型群的所有极大子群.对于典型群的研究-般有两种方法:几何方法和矩阵分析方法.主要对局部环上的辛群进行研究.设R是特征不为2的局部环,M是R的唯-极大理想,R/M表示其决定的剩余类域,m是正整数,Sp(2m,R)为R上的辛群.利用矩阵技巧和局部环的相关性质,主要讨论局部环R上辛群Sp(2m,R)的-类子群的结构,并获得其-类极大子群. |
| 英文摘要: |
| The classical group theory is an important part of group theory,and the symplectic group is one significant kind of such classical groups.The aim of research on subgroup structure of classical groups is to determine the maximal subgroups of all classical groups.There are two ways to study the classical groups: geometry technique and matrix theory.This paper mainly focuses on the subgroups of a symplectic group over a local ring.Let be a local ring,be the unique maximal ideal of,be the reside field of,be a positive integer,be the symplectic group over.In this paper,by applying matrix skills and the properties of local rings,we make some research on the subgroup structure of the symplectic groups over rings,particularly over the local rings,and obtain a type of maximal subgroup of symplectic groups. |
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