非次正规子群共轭类数对有限群结构的影响

doi:10.16088/j.issn.1001-6600.2017.01.007

广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (1): 44-48.doi: 10.16088/j.issn.1001-6600.2017.01.007

非次正规子群共轭类数对有限群结构的影响

钟祥贵,丁锐芳,凌思敏

广西师范大学数学与统计学院,广西桂林541004

出版日期:2017-01-20 发布日期:2018-07-17
通讯作者: 钟祥贵(1963—),男,湖南武冈人,广西师范大学教授。E-mail:xgzhong@gxnu.edu.cn
基金资助:
国家自然科学基金(11261007,11461007);广西自然科学基金(2014GXNSFAA118009);广西教育厅科研项目(ZD2014016,KY2015YB504)

Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups

ZHONG Xianggui, DING Ruifang, LING Simin

College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China

Online:2017-01-20 Published:2018-07-17

摘要/Abstract

摘要： 设G是有限群,π(G)表示G的阶的素因子集合,μ(G)表示G的非次正规子群的共轭类类数。本文证明了满足条件μ(G)≤2|π(G)|的有限群G可解,并完全刻画非次正规子群共轭类类数不大于群的阶的素因子个数的有限群,即满足不等式μ(G)≤|π(G)|的有限群G的结构。

关键词: 有限群;次正规子群;共轭类;可解群

Abstract: Let G be a finite group, π(G) be the set of prime factors dividing |G| and μ(G) denote the number of conjugacy classes of all non-subnormal subgroups of G. In this paper, it is shown that all finite groups G with μ(G)≤2|π(G)| are solvable and that the structure of finite groups having at most |π(G)| conjugacy classes of non-subnormal subgroups are completely characterized.

Key words: finite group, subnormal subgroup, conjugacy class, solvable groups

中图分类号:

O152.1

钟祥贵,丁锐芳,凌思敏. 非次正规子群共轭类数对有限群结构的影响[J]. 广西师范大学学报（自然科学版）, 2017, 35(1): 44-48.

ZHONG Xianggui, DING Ruifang, LING Simin. Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(1): 44-48.

参考文献

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[5] 冯爱芳, 段泽勇. 仅含两个非次正规子群共轭类的有限群[J]. 西南师范大学学报(自然科学版),2008, 33(5):7-10. DOI:10.13718/j.cnki.xsxb.2008.05.003.
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非次正规子群共轭类数对有限群结构的影响

Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups

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