子群的S-半置换性与有限群的p-超可解性

doi:10.12052/gdutxb.190122

广东工业大学学报 ›› 2020, Vol. 37 ›› Issue (04): 65-68.doi: 10.12052/gdutxb.190122

子群的S-半置换性与有限群的p-超可解性

邱正添, 乔守红

广东工业大学应用数学学院，广东广州 510520

收稿日期:2019-10-10 出版日期:2020-07-11 发布日期:2020-07-02
作者简介:邱正添(1994-)，男，硕士研究生，主要研究方向为有限群论，E-mail：1781108093@qq.com

S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group

Qiu Zheng-tian, Qiao Shou-hong

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China

Received:2019-10-10 Online:2020-07-11 Published:2020-07-02

摘要/Abstract

摘要： 令G为有限群, H是G的子群。称H是G的S-半置换子群, 如果对G的任意Sylow p-子群${G_p}$, 满足($p$, $\left| H \right|$)=1, 都有$H{G_p} = {G_p}H$。本文主要探讨子群的S-半置换性对有限群的$p$-超可解性的影响, 给出了一些关于有限群的$p$-超可解性的判定条件, 并对已知的结果进行了推广。

关键词: 有限群, p-超可解群, S-半置换子群

Abstract: Let G be a finite group, H is a subgroup of $G$. H is S-semipermutable in $G$, if $H{G_p} = {G_p}H$ for any prime divisor p of ${\rm{|}}G{\rm{|}}$ and Sylow p-subgroup ${G_p}$ with $(p, \left| H \right|) = 1$. The influence of the S-semipermutability of subgroups on the p-supersolubility of a finite group is investigated. Some interesting results are obtained which generalize some known results.

Key words: finite groups, p-supersoluble group, S-semipermutability

中图分类号:

O152

邱正添, 乔守红. 子群的S-半置换性与有限群的p-超可解性[J]. 广东工业大学学报, 2020, 37(04): 65-68.

Qiu Zheng-tian, Qiao Shou-hong. S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group[J]. Journal of Guangdong University of Technology, 2020, 37(04): 65-68.

参考文献

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子群的S-半置换性与有限群的p-超可解性

S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group

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