Journal of Guangdong University of Technology ›› 2020, Vol. 37 ›› Issue (04): 65-68.doi: 10.12052/gdutxb.190122

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

Qiu Zheng-tian, Qiao Shou-hong   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2019-10-10 Online:2020-07-11 Published:2020-07-02

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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.

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

CLC Number: 

  • O152
[1] HUPPERT B. Endliche gruppen I [M]. Berlin: Springer-Verlag, 1967.
[2] 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
[3] SKIBA A N. On weakly s-permutable subgroups of finite groups [J]. Journal of Algebra, 2007, 315(1): 192-209
[4] GUO X Y, ZHANG B R. Conditions on p-Subgroups implying p-Supersolvability [J]. Journal of Algebra and Its Applications, 2017, 16(10): 1750196
[5] 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
[6] BERKOVICH Y, ISAACS I M. p-Supersolvability and actions on p-groups stabilizing certain subgroups [J]. Journal of Algebra, 2014, 414: 82-94
[7] 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
[8] 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
[9] 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
[10] ISAACS I M. Semipermutable π-subgroups [J]. Archiv der Mathematik, 2014, 102(1): 1-6
[11] 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
[1] Tan Lihui, Qiao Shouhong. Finite Groups with Some c1-Supplemented Subgroups [J]. Journal of Guangdong University of Technology, 2012, 29(3): 46-48.
[2] QIAO Shou-Hong, GUO Da-Chang-. [J]. Journal of Guangdong University of Technology, 2011, 28(1): 54-57.
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