有限群极大子群的θ-子群偶  

On Theta Pairs for Maximal Subgroups of Finite Groups

作　　者：赵耀庆[1] 

机构地区：[1]广西大学数学系,南宁530004

出　　处：《数学学报（中文版）》1997年第1期67-72,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;广西教委基金

摘　　要：N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.In the paper 'On theta pairs for a maximal subgroup' (Proc. Amer. Math. Soc., V109N3(1990)), N.P. Mukherjee and P.Bhattacharya denned the concept of θ-pairs associated to a maximal subgroup of a finite group, studied the influence of θ-pairs on the structure of the group itself and obtained several results. In this paper we study first the further properties of θ-pairs, then improve in essence some of the main results in Mukherjee and Bhattacharya's paper by using these properties and deal with some new conditions which are necessary and sufficient for a group to be solvable or nilpotent.

关 键 词：有限群 极大子群 Θ-子群偶 可解性 幂零性 

分 类 号：O152.1[理学—数学]