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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 9-12.doi: 10.6040/j.issn.1671-9352.0.2024.304

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关于有限群中非σ-次正规子群数量的探讨

马小箭,毛月梅*   

  1. 山西大同大学数学与统计学院, 山西 大同 037009
  • 发布日期:2025-05-19
  • 通讯作者: 毛月梅(1979— ),女,教授,硕士生导师,博士,研究方向为群论. E-mail:maoyuemei@126.com
  • 作者简介:马小箭(1979— ),男,副教授,硕士,研究方向为群论. E-mail:mxj790808@163.com*通信作者:毛月梅(1979— ),女,教授,硕士生导师,博士,研究方向为群论. E-mail:maoyuemei@126.com
  • 基金资助:
    国家自然科学基金资助项目(12371021)

Discussion on the number of non σ-subnormal subgroups in finite groups

MA Xiaojian, MAO Yuemei*   

  1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, Shanxi, China
  • Published:2025-05-19

摘要: 设G是一个有限群,nσ(G)表示G中所有非σ-次正规子群共轭类的个数。利用极小阶反例的证明方法和σ-次正规的一些性质,比较nσ(G)与|σ(G)|的数量关系,给出了σ-可解群的一个新的结论,并由此推广了已有的一些成果。

关键词: σ-可解群, 非σ-次正规子群, Hall σi-子群, Sylow型的σ-完全群

Abstract: Let G be a finite group and nσ(G) be the number of conjugacy classes of all non σ-subnormal subgroups. Applying the proof method of minimal order counterexamples and some σ-subnormal properties, new conclusions of σ-solvable groups and generalize some previous results are given by comparing quantitative relationships between nσ(G) and |σ(G)|.

Key words: σ-solvable groups, non σ-subnormal subgroups, Hall σi-subgroups, σ-full group of Sylow type

中图分类号: 

  • O152
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[1] 马小箭, 毛月梅. 子群的σ-嵌入系统对有限群结构的影响[J]. 《山东大学学报(理学版)》, 2022, 57(2): 67-71.
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