子群的弱m-σ-置换性在饱和群系方面的应用  

The Application ofWeakly m-σ-permutability of Subgroups in Saturated Formation

作　　者：施智杰 马小箭 毛月梅 SHI Zhi-jie;MA Xiao-jian;MAO Yue-mei(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2023年第3期23-26,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目[11901364]。

摘　　要：设H为有限群G的子群,称H在G中是弱m-σ-置换的,如果存在着G的m-σ-置换子群S和σ-次正规子群T使得G=HT且H⋂T≤S≤H。为了探究有限群的结构,本文应用极小阶反例的证明方法和σ-次正规子群以及σ-置换子群的一些相关理论,研究了弱m-σ-置换子群对饱和群系的影响。通过讨论群G的Hallσi-子群的极大子群的弱m-σ-置换性,给出了群G属于所有超可解群构成的饱和群系的充分条件。Let G be a finite group.A subgroup H of G is said to be weakly m-σ-permutable in G,if there exists an m-σ-permut-able subgroup S and aσ-subnormal subgroup T in G such that G=HT and H⋂T≤S≤H.In order to explore the structure of finite groups,this paper applies the proof method of minimal order counter examples and some related theories ofσ-subnormal subgroups andσ-permutable subgroups to study the influence of weakly m-σ-permutable subgroups on saturated formation.Let F be a saturat-ed formation containing all supersoluble groups.The paper gives a sufficient condition that G∈by discussing weakly m-σ-per-mutablity of the maximal subgroups of Hallσi-subgroups of G.

关 键 词：有限群 弱m-σ-置换子群 σ-次正规子群 Hallσi-子群 

分 类 号：O152[理学—数学]