浙江大学学报（理学版）2024，Vol.51Issue(1)：1-4,20,5.DOI:10.3785/j.issn.1008-9497.2024.01.001
子群的完全置换性对σ-幂零根的影响
The influence of the totally permutability of subgroups on σ-nilpotent residual
摘要
Abstract
Similar to the influence on nilpotent residual of the totally permutability of subgroups,naturally,we can study their influence on σ-nilpotent residual when nilpotent groups are generalized to σ-nilpotent groups.The intersection of all normal subgroups N of G such that G/N is σ-nilpotent is called σ-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 ANσ and centralises ANσ by using the concepts and theories of σ-nilpotent subgroups and σ-supersoluble subgroups,and by applying some properties and methods of complete Hall σ-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Key words
σ-supersoluble groups/σ-nilpotent groups/totally permutablity/Sylow subgroups分类
数理科学引用本文复制引用
施智杰,毛月梅,马小箭..子群的完全置换性对σ-幂零根的影响[J].浙江大学学报（理学版）,2024,51(1):1-4,20,5.基金项目
国家自然科学基金资助项目(11901364,11971277) （11901364,11971277）
山西省应用基础研究计划资助项目(201901D211439). （201901D211439）
