﻿ 交换环上线性群中含根子群的极大子群 Maximal Subgroups Containing Root Subgroups in Linear Groups over Commutative Ring

Pure Mathematics
Vol.07 No.05(2017), Article ID:21747,5 pages
10.12677/PM.2017.75046

Maximal Subgroups Containing Root Subgroups in Linear Groups over Commutative Ring

Xin Hou*, Shangzhi Li

School of Mathematics and Systems Science, Beihang University, Beijing

*通讯作者。

Received: Aug. 3rd, 2017; accepted: Aug. 17th, 2017; published: Aug. 21st, 2017

ABSTRACT

The maximality of three types of subgroups containing root subgroups in linear groups is verified in this paper. And the possible types of maximal subgroups containing root subgroups in linear groups over commutative ring are discussed.

Keywords:Maximal Subgroups, Root Subgroups, Linear Groups, Commutative Ring

Copyright © 2017 by authors and Hans Publishers Inc.

1. 引言

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1) 存在的某个极大理想，使是域上线性群的极大子群。当时，一定是定理1的3类子群之一。

2) 对的每个极大理想都有

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2. 定理的证明

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Maximal Subgroups Containing Root Subgroups in Linear Groups over Commutative Ring[J]. 理论数学, 2017, 07(05): 363-367. http://dx.doi.org/10.12677/PM.2017.75046

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