Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (4): 54-58.doi: 10.16088/j.issn.1001-6600.2020.04.006

Previous Articles     Next Articles

On Generalized c#-subgroups of Finite Groups

WEI Huaquan1*, YUAN Weifeng1, ZHOU Yuzhen2, LI Xue1, LI Min1   

  1. 1. College of Mathematics and Information Science, Guangxi University, Nanning Guangxi 530004, China;
    2. Dean's Office, Guangxi University, Nanning Guangxi 530004, China
  • Received:2019-04-25 Published:2020-07-13

PDF (PC)

276

Abstract: A subgroup H of a finite group G is said to be a generalized c#-normal subgroup of G if there exists a normal subgroup K of G such that HK is normal in G and H∩K is a CAP-subgroup of G. By using the c#-normality of some Hall and maximal subgroups, several sufficient or necessary conditions are obtained for a group to be π-solvable or solvable.

Key words: finite group, generalized c#-normal subgroup, Hall subgroup, solvable group

CLC Number: 

  • O152.1
[1] GASCHÜTZ W. Praefrattinigruppen[J].Archiv der Mathematik,1962,13: 418-426.
[2] DOERK H, HAWKES T. Finite solvable groups[M].Berlin: Springer-Verlag, 1992.
[3] TOMKINSON M J. Cover-avoidance properties in finite soluble groups[J].Canadian Mathematics Bulleting,1976,19(2): 213-216.
[4] EZQUERRO L M. A contribution to the theory of finite supersolvable groups[J].Rendiconti del Seminario Matematico Della Universita Di Padova,1993,89: 161-170.
[5] GUO X Y, SHUM K P. Cover-avoidance properties and the structure of finite groups[J].Journal of Pure and Applications Algebra,2003,181: 297-308.
[6] 樊恽, 郭秀云, 岑嘉评. 关于子群的两种广义正规性注记[J].数学年刊,2006,27A(2): 169-176.
[7] WANG Y M. c-normality of groups and its properties[J].Journal of Algebra,1996,180(3): 954-965.
[8] 韦华全. 子群特性与有限群结构[D].广州: 中山大学, 2006.
[9] WANG Y M, WEI H Q. c#-normality of groups and its properties[J].Algebra Representation Theory, 2013,16(1): 193-204.
[10]WANG Y M, WEI H Q. On CAS-subgroups of finite groups[J].Israel Journal of Mathematics,2007, 159: 175-188.
[11]高辉,高胜哲,尹丽. 关于有限群子群的θ-完备[J].郑州大学学报(理学版),2016,48(2): 11-13.
[12]彭红,钟祥贵,谢青. 几乎SS-嵌入子群与有限群的p-幂零性[J].广西师范大学学报(自然科学版),2017,35(2): 45-49.
[13]卢家宽,邱燕燕.子群弱S-可补性对有限群可解性的影响[J].广西师范大学学报(自然科学版),2017,35(1): 49-52.
[14]吕玉博,韦华全,李敏. 几乎SS-嵌入子群对有限群p-幂零性的影响[J].广西师范大学学报(自然科学版),2019,37(1): 149-154.
[15]项容,吴勇,钟祥贵.NS*-拟正规子群与有限群的p-幂零性[J].广西师范大学学报(自然科学版),2015,33(4): 63-67.
[16]谢凤艳,闫俊娜.p-超可解群的若干充分条件[J].郑州大学学报(理学版),2014,46(4): 23-26.
[17]LU R F, WEI H Q, DONG S Q, et al. Finite groups with some X-semipermutable subgroups[J].Journal of Sichuan Normal University(Nalural Science),2013,36(1): 39-43.
[18]石向东,韦华全,马儇龙. 乘积因子群的共轭类长与有限群结构[J].郑州大学学报(理学版),2013,45(2): 10-13.
[19]卢若飞,韦华全,周宇珍, 等. 有限群共轭类长的一个问题[J].数学学报(中文版),2016,59(6): 795-798.
[20]卢家宽,刘雪霞,覃雪清. 关于Frobenius群的注记[J].广西师范大学学报(自然科学版),2018,36(1): 84-87.
[21]ROBINSON D J S. A course in the theory of groups[M].New York: Springer-Verlag, 1980.
[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] SUN Yuqing, LU Jiakuan. Influence of Self-centralizing Subgroups on the Structure of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(5): 48-55.
[3] ZHONG Xianggui, SUN Yue, WU Xianghua. Nearly CAP*-Subgroups and p-Supersolvability of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 74-78.
[4] LÜ Yubo, WEI Huaquan, LI Min. The Influence of Nearly SS-embedded Subgroups on the p-nilpotency of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(1): 149-154.
[5] LU Jiakuan,LIU Xuexia,QIN Xueqing. Notes on Frobenius Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 84-87.
[6] PENG Hong, ZHONG Xianggui, XIE Qing. Nearly SS-Quasinormal Subgroups and p-Nilpotency of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(2): 45-49.
[7] ZHONG Xianggui, DING Ruifang, LING Simin. Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(1): 44-48.
[8] LU Jiakuan, QIU Yanyan. The Influence of Weakly s-supplemented Subgroups on Solvability of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(1): 49-52.
[9] XIANG Rong, WU Yong, ZHONG Xiang-gui. NS*-quasinormal Subgroups and p-nilpotency of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(4): 63-67.
[10] SHI Jiang-tao, ZHANG Cui. Finite Non-solvable Groups with a Small Number of Conjugacy Classes of Non-trivial Cyclic Subgroups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(3): 52-56.
[11] WU Yong, ZHONG Xiang-gui, JIANG Qing-zhi, ZHANG Xiao-fang. CSS-Quasinormal Subgroups and p-Nilpotency of Finite Groups [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(2): 60-63.
[12] 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.
[13] ZHONG Xiang-gui, LI Yong-gang, ZHANG Fu-sheng, WUYong. Finite Nilpotent Groups with Automorphism Group of Order 16p1p2…pr [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(2): 58-63.
[14] 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.
[15] SHI Jiang-tao, ZHANG Cui, GUO Song-tao. A Note on Theorem of Shlyk [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 22-24.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LIU Ming, ZHANG Shuangquan, HE Yude. Classification Study of Differential Telecom Users Based on SOM Neural Network[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 17 -24 .
[2] HUANG Bingfang,WEN Binghai,QIU Wen,ZHAO Wanling,CHEN Yanyan. Research on Real Time Measurement of Contact Angle Based on Lattice Boltzmann Method[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 34 -43 .
[3] ZHANG Junwen. Determination of Oleanic Acid and Uosolic Acid in Gentiana straminea Maxim. by MEKC[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 99 -104 .
[4] QIN Ying. A Newly Recorded Genus of Polygalaceae from Guangxi,China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 126 -128 .
[5] ZHANG Haoran. Benthic Diatom Assemblages Distribution in Longjiang and Diaojiang Rivers, in Relation to Chemical and Physiographical Factor[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 132 -141 .
[6] XU Weifeng,YAO Feihua, LIANG Xuefeng, ZHENG Na, YANG Ruiyun,LI Jun. Secondary Metabolites of Endophytic Fungus GDG-180 from Sophora tonkinensis[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(1): 58 -61 .
[7] WEI Jianhua, XI Qingnan, LI Bing, LIAO Pengying, HUO Lini, LU Rumei. Chemical Constituents from a Zhuang Medicine of Jasminum nervosum Lour.[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 94 -97 .
[8] QIU Qin,YU Lifeng,CHEN Mingwei,ZHEN Dandan,HUANG Lijing,ZHEN Hanshen,XU Yuhua. Determination of Quercetin, Kaempferol and Rhamnolipid in Stem and Leaf of Sedum emarginatum Migo by HPLC[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 98 -104 .
[9] ZHANG Fangliang, DENG Xiaohong, ZHU Xiaotong, XU Lei, HU Jiangli, BIN Shiyu. Cloning and Expression Analysis of Ubiquitin-Specific Protease 7 Gene under Starvation in Mandarin Fish (Siniperca chuatsi)[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 141 -147 .
[10] LIU Jiali. Alterations in Regional Homogeneity of Resting-state Brain Activity in Chronic Cigarette Smokers[J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(4): 151 -155 .
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