某些C-S-置换子群对有限群结构的影响
Influence of Certain C-S-Permutable Subgroups on the Structure of Finite Groups

作者: 何宣丽 :广西大学数学与信息科学学院; 王燕鸣 :中山大学岭南学院,数学与计算科学学院;

关键词: C-S-置换子群广义Fitting子群群系C-S-Permutable Subgroup Generalized Fitting Subgroup Formation

摘要:
H为有限群G的子群,CG的非空子集。记。如果对G的每个Sylow子群T,都存在某个使得,则称HG中是C-S-置换的(共轭-Sylow-置换的)。本文,我们研究有限群G的某些C-S-置换子群对G的结构的影响,改进并推广了最近的一些结果。


Abstract:
Let H be a subgroup of a finite group G and C a nonempty subset of G. Denote . H is said to be C-S-permutable (Conjugate-Sylow-permutable) in G, if, for every Sylow subgroup T of G, there exists some element such that . In this paper, we study the influence of certain C$-S-permutable subgroups of the finite group G on its structure. Some recent results are improved and extended.

文章引用: 何宣丽 , 王燕鸣 (2013) 某些C-S-置换子群对有限群结构的影响。 理论数学, 3, 126-132. doi: 10.12677/PM.2013.32020

参考文献

[1] B. Huppert. Endliche Gruppen I. Berlin, Heidelberg, New York: Springer-Verlag, 1967.

[2] O. H. Kegel. Sylow-Gruppen und subnormalteiler endlicher Gruppen. Mathematische Zeitschrift, 1962, 78: 205-221.

[3] S. Srinivasan. Two sufficient conditions for supersolvability of finite groups. Israel Journal of Mathematics, 1980, 35: 210-214.

[4] Z. Arad, M. B. Ward. New criteria for the solvability of finite groups. Journal of Algebra, 1982, 77: 234-246.

[5] Y. Li, Y. Wang and H. Wei. The influence of π-quasinormality of some subgroups of a finite group. Archiv der Mathematik (Basel), 2003, 81(3): 245-252.

[6] B. Huppert, N. Blackburn. Finite groups III. Berlin, New York: Springer-Verlag, 1982.

[7] H. Wei, Y. Wang and Y. Li. On c-normal maximal and minimal subgroups of Sylow subgroups of finite groups II. Communications in Algebra, 2003, 31(10): 4807-4816.

[8] Y. Li, Y. Wang. On π-quasinormally embedded subgroups of finite group. Journal of Algebra, 2004, 281: 109-123.

[9] M. Asaad and A. A. Heliel. On S-quasinormal embedded subgroups of finite groups. Journal of Pure and Applied Algebra, 2001, 165: 129-135.

[10] M. Asaad. On maximal subgroups of Sylow subgroups of finite groups. Communications in Algebra, 1998, 26(11): 3647-3652.

分享
Top