Journal of Guangxi Normal University(Natural Science Edition) ›› 2010, Vol. 28 ›› Issue (1): 13-17.

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Deskins Index Complex and Solvability of Finite Groups

WANG Cun-cai, ZHANG Hong, ZHONG Xiang-gui   

  1. College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2009-09-01 Online:2010-03-20 Published:2023-02-07

Abstract: By using the theories of the Deskins index complex ofthe maximal subgroup of finite groups,some relational theorems in the relevantreference are continued,and two new criteria of the solvable groups are obtained.

Key words: finite groups, maximal subgroups, maximal completion, p-rank, solvability groups

CLC Number: 

  • O152.1
[1] 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):38-41.
[2] 刘熠,曾意,王坤仁.S-拟正规子群对有限群结构的影响[J].四川师范大学学报:自然科学版,2009,32(1):39-42.
[3] 王长群,杨晓梅.有限群中的子群和元素的共轭性质[J].郑州大学学报:理学版,2005,37(3):28-30.
[4] DESKINS W E.A note on the index complex of a maximal subgroup[J].Arch Math:Basel,1990,54:236-240.
[5] ZHANG Yue-ming,BALLESTER-BOLINCHES A,GUO Xiu-yun.On the Deskinsindex complex of a maximal subgroup of a finite group[J].J Pure and Appl Algebra,1999,136(3):211-216.
[6] LI Shi-rong,ZHAO Yao-qing.The Deskins index complex and the solvability of finite groups[J].Southeast Asian Bulletin of Mathematics,1998,22:291-299.
[7] LI Shi-rong.The Deskins index complex and the supersolvability of finite groups[J].J Pure and Appl Algebra,1999,144:297-302.
[8] GURALNICK R M.Subgroups of prime power index in a simple group[J].JAlgebra,1983,81:304-311.
[9] GORENSTEIN D.Finite groups[M].New York:Chelsea,1980.
[10] 徐明曜.有限群导引(上册)[M].北京:科学出版社,2001.
[11] 李世荣.有限群的Deskins极大完备[J].数学年刊,2003,24A(2):145-150.
[12] 徐明曜.有限群导引(下册)[M].北京:科学出版社,2001.
[13] BAER R.Classes of finite groups and their properties[J].Illinois JMath,1957,1:115-187.
[14] 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.
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[2] 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.
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