子群的<i>S</i>-半置换性与有限群的<i>p</i>-超可解性

邱正添; 乔守红

doi:10.12052/gdutxb.190122

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子群的S-半置换性与有限群的p-超可解性

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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
- 广东工业大学学报 2020年37卷第4期页码：65-68
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 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
- 基金信息：
- DOI：10.12052/gdutxb.190122
  中图分类号： O152
- 网络首发：2020-07-11，
  
  纸质出版：2020
- 稿件说明：
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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.

Qiu Zheng-tian, Qiao Shou-hong. S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group[J]. 2020, 37(4): 65-68. DOI: 10.12052/gdutxb.190122.
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. DOI： 10.12052/gdutxb.190122.

Qiu Zheng-tian, Qiao Shou-hong. S-Semipermutability of Subgroups and p-Supersolubility of a Finite Group[J]. 2020, 37(4): 65-68. DOI: 10.12052/gdutxb.190122. DOI：

摘要

令

为有限群

是

的子群。称

是

的

-半置换子群

如果对

的任意Sylow

-子群

${G_p}$

img text_id='M10' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M10.jpg'>

满足(

$p$

img text_id='M11' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M11.jpg'>

$\left| H \right|$

img text_id='M12' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M12.jpg'>

)=1

都有

$H{G_p} = {G_p}H$

img text_id='M13' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M13.jpg'>

。本文主要探讨子群的

italic/>

-半置换性对有限群的

$p$

img text_id='M11' class='formula-im

g' style='display:none;' src='gdgydxxb-37-4-65_M11.jpg'>

-超可解性的影响

给出了一些关于有限群的

$p$

img text_id='M11' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M11.jpg'>

-超可解性的判定条件

并对已知的结果进行了推广。

Abstract

Let

be a finite group

is a subgroup of

$G$

img text_id='M19' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M19.jpg'>

-semipermutable in

$G$

img text_id='M19' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M19.jpg'>

$H{G_p} = {G_p}H$

img text_id='M22' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M22.jpg'>

for any prime divisor

${\rm{|}}G{\rm{|}}$

img text_id='M23' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M23.jpg'>

and Sylow

-subgroup

${G_p}$

img text_id='M24' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M24.jpg'>

with

$(p

\left| H \right|) = 1$

img text_id='M25' class='formula-img' style='display:none;' src='gdgydxxb-37-4-65_M25.jpg'>

. The influence of the

-semipermutability of subgroups on the

-supersolubilit

y of a finite group is investigated. Some interesting results are obtained which generalize some known results.

关键词

Keywords

references

HUPPERT B. Endliche gruppen I [M]. Berlin: Springer-Verlag, 1967.

WANG L F, WANG Y M. On s -semipermutable maximal and minimal subgroups of Sylow p -Subgroups of finite groups [J ] . Communications in Algebra, 2006, 34(1): 143-149.

SKIBA A N. On weakly s -permutable subgroups of finite groups [J ] . Journal of Algebra, 2007, 315(1): 192-209.

GUO X Y, ZHANG B R. Conditions on p -Subgroups implying p -Supersolvability [J ] . Journal of Algebra and Its Applications, 2017, 16(10): 1750196.

LI Y M, QIAO S H, SU N, et al . On weakly s -semipermutable subgroups of finite groups [J ] . Journal of Algebra, 2012, 371: 250-261.

BERKOVICH Y, ISAACS I M. p -Supersolvability and actions on p -groups stabilizing certain subgroups [J ] . Journal of Algebra, 2014, 414: 82-94.

MIAO L Y, LI Y M. Some criteria for p -Supersolvability of a finite group [J ] . Communications in Mathematics and Statistics, 2017, 5(3): 339-348.

ZHANG B R, GUO X Y. A note on the embedding properties of p -Subgroups in finite groups [J ] . Hacettepe Journal of Mathematics and Statistics, 2019, 48(1): 102-111.

YU H R. Some sufficient and necessary conditions for p -Supersolvablity and p -nilpotence of a finite group [J ] . Journal of Algebra and Its Applications, 2017, 16(2): 1750052.

ISAACS I M. Semipermutable π -subgroups [J ] . Archiv der Mathematik, 2014, 102(1): 1-6.

SHEN J X, QIAO S H. p -Supersoluble hypercenter and s -semipermutability of subgroups of a finite group [J ] . Bulletin of the Iranian Mathematical Society, 2018, 44(5): 1185-1193.

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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

DOI：10.12052/gdutxb.190122

摘要

Abstract

关键词

Keywords

references