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有限群极大子群的θ-子群偶
引用本文:赵耀庆.有限群极大子群的θ-子群偶[J].数学学报,1997,40(1):67-72.
作者姓名:赵耀庆
作者单位:广西大学数学系 南宁530004
基金项目: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.

关 键 词:有限群  极大子群  极大子群的θ-子群偶
收稿时间:1993-12-10
修稿时间:1996-2-27

On Theta Pairs for Maximal Subgroups of Finite Groups
Zhao Yaoqing.On Theta Pairs for Maximal Subgroups of Finite Groups[J].Acta Mathematica Sinica,1997,40(1):67-72.
Authors:Zhao Yaoqing
Institution:Zhao Yaoqing (Department of Mathematics, Guangxi University, Nanning 530004, China)
Abstract: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.
Keywords:Finite groups  Maximal subgroups  φ-pairs for maximal subgroups
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