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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
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
关键词
有限群
极大子群
Θ-子群偶
可解性
幂零性
Finite groups, Maximal subgroups, φ-pairs for maximal subgroups
