引用本文:曹建基, 高建玲.非正规循环子群的正规化子皆极大的两类有限可解群[J].西南大学学报(自然科学版),2018,40(12):81~85
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非正规循环子群的正规化子皆极大的两类有限可解群
曹建基, 高建玲1,2
1. 山西财经大学 应用数学学院, 太原 030006;2. 山西大同大学 数学与统计学院, 山西 大同 037009
摘要:
子群的正规性和有限群的结构有密切的关系,而正规化子作为子群正规性的一种度量对有限群结构的影响自然也很大.极大子群是有限群的一类重要子群.利用某些子群的正规化子的极大性研究有限群的结构.具体研究了群G的阶被p整除的非正规循环子群的正规化子皆极大的有限可解群,以及非正规p-子群和{p,q}-子群的正规化子均极大的有限可解群.得到这两类群的一些性质,并对这两类群的结构给出了刻画.
关键词:  极大子群  正规子群  正规化子
DOI:10.13718/j.cnki.xdzk.2018.12.012
分类号:O152.1
基金项目:国家自然科学基金项目(11801334);2018年引进博士启动经费项目(Z18207).
Two Finite Solvable Groups in Which the Normalizer of Some Non-Normal Subgroups is Maximal
CAO Jian-ji, GAO Jian-ling1,2
1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China;2. School of Mathematics and Statistics, Shanxi Datong University, Datong Shanxi 037009, China
Abstract:
The normality of subgroups is closely related to the structure of finite groups, and the normalizer of subgroups, which is a measure of the normality of subgroups, has a significant influence on their structure. On the other hand, the maximal subgroup is an important kind of subgroup of finite groups. So it is reasonable to investigate the structure of a group by using normalizers of some kind of subgroups. In this paper, we study the solvable groups in which the normalizer of cyclic subgroups whose order is divided by p is maximal in G. We also study the solvable groups in which every non-normal p-subgroup and {p, q}-subgroup have a maximal normalizer in G. Some good properties are given for the above two types of group, and we also describe the structure of the two types of group.
Key words:  maximal subgroup  normal subgroup  normalizer
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