广西师范大学学报（自然科学版）2017，Vol.35Issue(1)：49-52,4.DOI:10.16088/j.issn.1001-6600.2017.01.008
子群弱s-可补性对有限群可解性的影响
The Influence of Weakly s-supplemented Subgroups on Solvability of Finite Groups
摘要
Abstract
A subgroup H of a finite group G is called weakly s-supplemented subgroup of G if there is a subgroup K of G such that G=HK and H∩K≤HsG ,where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G.In this paper,the following results are proved:(1) a finite group G is solvable if every subgroup of odd prime order of G is weakly s-supplemented in G;(2)a finite group G is solvable if and only if every Sylow subgroup of odd order of G is weakly s-supplemented in G.Some classical and recent results are extended.关键词
弱s-可补子群/可解群/超可解群Key words
weakly s-supplemented subgroup/solvable group/supersolvable group分类
数理科学引用本文复制引用
卢家宽,邱燕燕..子群弱s-可补性对有限群可解性的影响[J].广西师范大学学报（自然科学版）,2017,35(1):49-52,4.基金项目
国家自然科学基金(11461007) （11461007）
广西高校数学与统计模型重点实验室开放基金(2016GXKLMS002) （2016GXKLMS002）
