几乎SS-嵌入子群与有限群的p-幂零性  

Nearly SS-Quasinormal Subgroups and p-Nilpotency of Finite Groups

作　　者：彭红[1] 钟祥贵[1] 谢青[1] 

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2017年第2期45-49,共5页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11261007;11461007);广西自然科学基金(2014GXNSFAA118009;2016GXNSFAA380156);广西高校科学技术研究项目(ZD2014016)

摘　　要：设G是有限群,子群H称为在G中几乎SS-嵌入的,如果存在G的S-拟正规子群K使得HK是G的S-拟正规子群,且H∩K≤H_(seG),这里H_(seG)是由包含在H中G的所有S-拟正规嵌入子群生成的群。本文应用Sylow p-子群的n-极大子群的几乎SS-嵌入性质刻画有限群的p-幂零性,统一和推广了以往的一些结果。Let G be a finite group. A subgroup H of G is said to be nearly SS-quasinormal in G if G has a S-quasinormal subgroup K such that HK is S-quasinormal in G, and H∩K≤HseG, where HseG is the subgroup of H generated by all those subgroups of H which are SS-quasinormal in G. In this paper, by using the nearly SS-quasinormalility of n-maximal subgroups of some Sylow p-subgroup of G, some new characterizations of p-nilpotent groups are obtained and several known results are generalized.

关 键 词：有限群 几乎SS-嵌入子群 P-幂零群 

分 类 号：O152.1[理学—数学]