On Theta Pairs for Maximal Subgroups of Finite Groups
YaoQing Zhao
Author information+
Zhao Yaoqing
(Department of Mathematics, Guangxi University, Nanning 530004, China)
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文章历史+
收稿日期
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出版日期
1993-12-10
1996-02-27
1997-01-15
发布日期
1997-01-15
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.
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.
YaoQing Zhao.
On Theta Pairs for Maximal Subgroups of Finite Groups. Acta Mathematica Sinica, Chinese Series, 1997, 40(1): 67-72 https://doi.org/10.12386/A1997sxxb0009