| 子群的S-半置换性与有限群的p-超可解性 |
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| 引用本文： | 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(4):65-68. |
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| 作者姓名： | 邱正添 乔守红 |
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| 作者单位： | 广东工业大学 应用数学学院，广东 广州 510520 |
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| 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。
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| 关 键 词： | 有限群 p-超可解群 S-半置换子群 |
| 收稿时间： | 2019-10-10 |
S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group |
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| 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(4):65-68. |
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| Authors: | Qiu Zheng-tian Qiao Shou-hong |
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| Affiliation: | School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China |
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| 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. |
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| Keywords: | finite groups p-supersoluble group S-semipermutability |
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