有限群的m-S-可补子群  

Finite groups with some m-S-supplemented subgroups

作　　者：刘鑫 吴珍凤 杨南迎[1] LIU Xin;WU Zhen-feng;YANG Nan-ying(School of Science,Jiangnan University,Wuxi 214122,Jiangsu,China)

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《山东大学学报（理学版）》2021年第4期8-13,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11771409)。

摘　　要：令G是一个有限群。群G的子群S称为在G中是m-S-置换的,如果存在着G的模子群A和S-置换子群B使得S=〈A,B〉。群G的子群H称为在G中是m-S-可补的,如果存在着G的m-S-置换子群S和G的子群T使得G=HT且H∩T≤S≤H。通过研究m-S-可补子群对有限群结构的影响,得到了有限群的p-幂零性和超可解性的一些新的判别准则,并推广了一些已得到的结果。Let G be a finite group. A subgroup S of G is said to be m-S-permutable in G,if S =〈A,B〉for some modular subgroup A and S-permutable subgroup B of G. A subgroup H of G is said to be m-S-supplemented in G,if there are an m-S-permutable subgroup S and a subgroup T of G such that G = HT and H ∩T≤S≤H. By using the m-S-supplemented subgroups to characterize the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained and generalize some known results.

关 键 词：有限群 模子群 S-置换子群 m-S-置换子群 m-S-可补子群 

分 类 号：O152[理学—数学]