利用极大子群的正规指数判定有限群的可解性
Using normal index of maximal subgroups to verdict the solvability of finite groups
摘要
从几类特殊的极大子群出发,利用极大子群的正规指数来刻划有限群G的可解性.
The solvability of finite group was characterized by using normal index of several kinds of maximal subgroups which ware defined by the author of this paper.
出处
《湖北大学学报（自然科学版）》
CAS
北大核心
2011年第2期221-223,244,共4页
Journal of Hubei University：Natural Science
关键词
有限群
极大子群
正规指数
可解性
finite group
maximal subgroup
normal index
the solvability
参考文献10
-
1Deskins W E. On maximal subgroups [J]. Proc Symp Pure Math Amer Math Soc, 1959(1) :100-104.
-
2Beidleman J C, Spencer A E. The normal index of maximal subgroups in finite groups [J]. Illinois J Math, 1972,16: 95-101.
-
3Mukheriee N P, Prabir Bhattacharya. The normal index of a finite group[J]. Pacific Journal of Mathematics, 1988, 1321143-149.
-
4Mukherjee N P, Prabir Bhattacharya. The normal index of a finite group[J]. Proceedings of the America Mathematics Society, 1989,106(1) :173-178.
-
5Wang Yanming. C-normal of groups and its properties[J].Journal of Algebra, 1996,180(3) : 954-965.
-
6Guo Xiuyun, Shum K P. Cover-avoidance properties and the strucute of finite group[J]. Journal of Pure and Applied Algebra, 2000,181 : 297-308.
-
7Mukherjee N P, Bhattacharya P. On the interseetion of a class of maximal subgroups of a finite group[J]. Can J Math, 1987,39:603-611.
-
8王品超,杨兆兴.有限群的极大子群的正规指数[J].工程数学学报,1994,11(1):42-48. 被引量：17
-
9Rose J S. On finite insoluble groups with nilponent maximal subgroups[J].J Algebra, 1977,48(1):182-196.
-
10Zhao Yaoqing. On the deskins completions for maximal subgroups[J]. Communication in Algebra, 2000,28 (1): 375-385.
共引文献16
-
1杨立英.有限群超可解及幂零的条件[J].广西师范学院学报（自然科学版）,2004,21(3):9-11.
-
2杨立英.有限群可解、超可解及幂零的充要条件[J].广西师范学院学报（自然科学版）,2004,21(4):26-28.
-
3杨立英.有限群可解的几个充要条件[J].广西师范学院学报（自然科学版）,2005,22(2):1-3. 被引量：1
-
4唐曾林,钟祥贵,黄雨星.有限可解群的CI-截刻画[J].广西科学,2007,14(3):196-199.
-
5杨立英.关于有限群可解的几个充要条件[J].广西大学学报（自然科学版）,1997,22(4):315-318.
-
6唐再良.有限群极大子群的正规指数与群的可解性[J].四川师范大学学报（自然科学版）,2008,31(4):410-413.
-
7李世荣,周龙桥,农国平,何俊.有限可解群的新刻画[J].广西科学,2008,15(4):330-333. 被引量：2
-
8王晓静,刘秋香,王品超.有限群的一类Frattini-Like子群[J].曲阜师范大学学报（自然科学版）,1998,24(1):1-4. 被引量：2
-
9杨立英.极大子群的θ-子群偶对群结构的影响[J].广西师院学报（自然科学版）,1999,16(4):9-14.
-
10王晓静,温凤桐.有限群的极大子群的正规指数[J].山西大学学报（自然科学版）,2001,24(2):104-106.
