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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 25-32.doi: 10.6040/j.issn.1671-9352.0.2023.430

• 群论 • 上一篇    

σ-置换嵌入子群对群p-幂零性的影响

吉九州,周伟,杨南迎*   

  1. 江南大学理学院, 江苏 无锡 214122
  • 发布日期:2025-05-19
  • 通讯作者: 杨南迎(1981— ),男,副教授,硕士生导师,博士,研究方向为有限群论及群类理论. E-mail:yangny@jiangnan.edu.cn
  • 作者简介:吉九州(1999— ),男,硕士研究生,研究方向为有限群论. E-mail:18601502750@163.com*通信作者:杨南迎(1981— ),男,副教授,硕士生导师,博士,研究方向为有限群论及群类理论. E-mail:yangny@jiangnan.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12201252)

Influence of σ-permutably embedded subgroups on p-nilpotency of finite groups

JI Jiuzhou, ZHOU Wei, YANG Nanying*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Published:2025-05-19

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摘要： G是一个有限群,称G的子群A在G中是σ-置换的,如果群G有一个完全Hall σ-集H,使得对所有的H∈H和所有的x∈G,均有AH x=H xA。称G的子群H在G中是σ-置换嵌入的,如果H的每个Hall σi-子群也是G的某个σ-置换子群的Hall σi-子群,研究群G的Sylow p-子群的σ-置换嵌入子群,给出群G为p-幂零群的新的判别准则。

关键词: 有限群, σ-置换子群, σ-置换嵌入子群, p-幂零群

Abstract: Let G be a finite group. A subgroup A of G is said to be σ-permutable in G if G possesses a complete Hall σ-set H such that AH x=H xA for all H∈H and all x∈G. A subgroup H of G is said to be σ-permutably embedded in G if every Hall σi-subgroup of H is also a Hall σi-subgroup of some σ-permutable subgroup of G. By studying the σ-permutably embedded subgroups of Sylow p-subgroups of G, some new criteria for G to be a p-nilpotent group are given.

Key words: finite group, σ-permutable subgroup, σ-permutably embedded subgroup, p-nilpotent group

中图分类号: 

  • O152
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