JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 9-12.doi: 10.6040/j.issn.1671-9352.0.2024.304

• Group Theory • Previous Articles    

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

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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

CLC Number: 

  • O152
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[1] MA Xiao-jian, MAO Yue-mei. Influence of σ-embedding system of subgroups on the structure of finite groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 67-71.
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