子群的完全置换性对σ-幂零根的影响  

The influence of the totally permutability of subgroups onσ-nilpotent residual

作　　者：施智杰 毛月梅 马小箭 SHI Zhijie;MAO Yuemei;MA Xiaojian(School of Mathematics and Statistics,Shanxi Datong University,Datong 037009,Shanxi Province,China)

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：《浙江大学学报（理学版）》2024年第1期1-4,20,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11901364,11971277);山西省应用基础研究计划资助项目(201901D211439).

摘　　要：先将幂零群推广为σ-幂零群,再研究子群的完全置换性对σ-幂零上根的影响。群G的所有使G/N为σ-幂零群的正规子群N的交称为G的σ-幂零上根,记为GNσ。设G=AB,其中A与B是完全置换的,利用子群的完全置换性质、σ-超可解群与σ-幂零群的概念和相关理论、完备Hallσ-集的性质以及有限群论的一些基本方法,给出了B正规化A的σ幂零根和中心化A的σ-幂零根的一些新的结论。Similar to the influence on nilpotent residual of the totally permutability of subgroups,naturally,we can study their influence onσ-nilpotent residual when nilpotent groups are generalized toσ-nilpotent groups.The intersection of all normal subgroups N of G such that G/N isσ-nilpotent is calledσ-nilpotent residual of G,and is denoted as GNσ.Let G=AB,where A and B are totally permutable subgroups of G,this paper gives some new conclusions that B normalises ANσand centralises ANσby using the concepts and theories ofσ-nilpotent subgroups andσ-supersoluble subgroups,and by applying some properties and methods of complete Hallσ-set and finite group theory.

关 键 词：σ-超可解群 σ-幂零群 完全置换性 SYLOW子群 

分 类 号：O152.1[理学—数学]