Journal of Guangxi Normal University(Natural Science Edition) ›› 2010, Vol. 28 ›› Issue (2): 34-37.

Previous Articles     Next Articles

F -Subgroups and Supersolubility of Finite Groups

ZHONG Xiang-gui, ZHANG Hong, HE Jia-wen   

  1. College of Mathematical Sciences,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2010-01-07 Online:2010-06-20 Published:2023-02-07

Abstract: Let F be a class of groups.A subgroup Hof a group G is called the F -subgroup of G if there exists a normal subgroup B of G such that HB —G,B/(B∩HG)∈F and B contains a Sylow q-subgroup of G for any prime q with (q,｜H｜)=1.By using F -subgroups of prime powerorder,this paper provides some sufficient conditions for G to be supersolvable.

Key words: F -subgroups, supersolvable groups, saturated formations

CLC Number: 

  • O152.1
[1] WANG Yan-ming.C-normality of groups and its properties[J].JAlgebra,1996,180(3):954-965.
[2] GUO Wen-bin.On F-supplemented subgroups of finite groups[J].Manuscripta Math,2008,127(2):139-150.
[3] WEI Hua-quan.On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups[J].Comm Algebra,2001,29(5):2193-2200.
[4] ZHONG Xiang-gui.Finite groups with some subgroups of prime powerorder c-supplemented[J].Indian J Pure Appl Math,2009,40(4):267-273.
[5] 钟祥贵,郭静安,单俊辉,等.共轭可置换子群对群结构的影响[J].广西师范大学学报:自然科学版,2008,26(1):38.
[6] 李长稳,郭文彬.关于F-S-可补子群[J].数学研究与评论,2007,27(1):207-211.
[7] 徐明曜.有限群导引(上册)[M].2版.北京:科学出版社,2001:130-175.
[8] 陈重穆.内外-Σ群与极小非-Σ群[M].重庆:西南师范大学出版社,1988:57-61.
[1] WU Xianghua, ZHONG Xianggui. Influence of NS*-permutable Subgroups on the Structure of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(5): 42-47.
[2] PANG Lin-na, QIU Yan-yan, LU Jia-kuan. On Some Sufficent Conditions of p-Nilpotency of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(2): 64-66.
[3] ZHONG Xiang-gui, LIAO Shu-hua, LI Ming-hua, TAN Chun-gui, CHEN Xiao-xiang. Maximal Supersolvable Subgroups and Supersolubility of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(3): 44-47.
[4] LU Jia-kuan, MENG Wei. On π-quasinormal Subgroup of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 35-37.
Viewed
Full text
14
HTML PDF
Just accepted Online first Issue Just accepted Online first Issue
0 0 0 0 0 14

  From local
  Times 14
  Rate 100%

Abstract
130
Just accepted Online first Issue
0 0 130
  From Others local
  Times 122 8
  Rate 94% 6%

Cited
Web of Science  Crossref   ScienceDirect  Search for Citations in Google Scholar >>
 
This page requires you have already subscribed to WoS.
  Shared   
  Discussed   
[1] CHEN Yong-qi, BAI Ke-zhao, KUANG hua, KONG Ling-jiang, LIU Mu-ren. Effect of Internal Layout on the Pedestrian Evacuation in the Classroom[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 1 -4 .
[2] XU Lun-hui, YE Fan. Acceleration Noise Model Based on Horizontal,Vertical and LateralAcceleration[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 5 -9 .
[3] YANG Li, KONG Ling-jiang. Capillary Force between Microparticles[J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 1 -4 .
[4] HE Qing, LIU Jian, WEI Lianfu. Single-Photon Detectors as the Physical Limit Detections of Weak Electromagnetic Signals[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(5): 1 -23 .
[5] BAI Ke-zhao, LUO Xu-dong, KONG Ling-jiang, LIU Mu-ren. Cellular Automaton Model of Date Transmission with Open Boundary Condition[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 1 -4 .
[6] XU Lun-hui, LIAO Ran-kun. Signal Phasing-Sequence Optimization of Intersection Based on Traffic Track[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 5 -9 .
[7] WANG Xiu-xin, QIN Li-mei, NONG Jing-hui, LIANG Zong-jin, ZHU Qi-jiang. Land Surface Temperature Retrieval with Mono-window Algorithm in Karst City[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 10 -14 .
[8] LI Yu-fang, ZHANG Jun-jian. Strong Consistency of the Regression Weighted Function Estimator for Negatively Associated Samples[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 15 -19 .
[9] JIA Bao-hua. A Strictly Stationary Associated Random Sequence Which Unsatisfythe Central Limit Theorem[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 20 -23 .
[10] CHEN Cui-ling, LI Ming, LIANG Jia-mei, LI Lüe. A Class of New Conjugate Gradient Method and Its Convergence Property Under the Wolfe Line Search[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 24 -28 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd