某些子群为CSS-子群的有限群  

Finite Groups with Some CSS-Subgroups

作　　者：刁倩玉 刘建军[1] DIAO Qianyu;LIU Jianjun(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第9期14-18,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971391);中央高校基本科研业务费项目(XDJK2020B052)。

摘　　要：设H为有限群G的一个子群,如果存在G的正规子群K,使得G=HK,且H∩K是G的SS-拟正规子群,则称H为G的CSS-子群.该文研究了有限群G的Sylow子群的部分极大子群为CSS-子群或S-拟正规嵌入子群时群的结构,得到了有限群为p-超可解群及p-幂零群的一些充分条件,推广了已有的结论.Let H be a subgroup of a finite group G.H is called a CSS-subgroup of G if there exists a normal subgroup K of G such that G=HK and H∩K is a SS-quasinormal subgroup.In this paper,we investigate the structure of G by supposing that some maximal subgroups of the Sylow subgroups of G are CSS-subgroups or S-quasinormally embedded subgroups,and obtain some sufficient conditions for a finite group to be p-supersolvable or p-nilpotent,generalizing some known results.

关 键 词：CSS-子群 S-拟正规嵌入子群 P-超可解群 P-幂零群 

分 类 号：O152.1[理学—数学]