摘要
称有限群G的子群H为弱s-可补子群,如果存在G的子群K,使得G=HK,H∩K≤H_(sG),其中H_(sG)是由H的在G中s-置换的子群生成的子群。本文证明了如下结果:1如果有限群G的奇素数阶子群在G中弱s-可补,那么G是可解群;2有限群G是可解群当且仅当G的所有奇数阶Sylow子群在G中弱s-可补。这2个结果推广和改进了已有的结果。
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.
出处
《广西师范大学学报（自然科学版）》
CAS
北大核心
2017年第1期49-52,共4页
Journal of Guangxi Normal University:Natural Science Edition
基金
国家自然科学基金(11461007)
广西高校数学与统计模型重点实验室开放基金(2016GXKLMS002)
关键词
弱s-可补子群
可解群
超可解群
weakly s-supplemented subgroup
solvable group
supersolvable group
