有限CN-群与有限c-可补群  

On Finite CN-Groups and Finite c-Supplemented Groups

作　　者：李样明[1] 赵立博[1] LI Yangming;ZHAO Libo(College of Mathematics,Guangdong University of Education,Guangzhou 510310,China)

机构地区：[1]广东第二师范学院数学学院,广州510310

出　　处：《数学年刊（A辑）》2021年第4期379-392,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12071092,No.12101135);广东省基础研究及应用研究重大项目(No.2017KZDXM058);广州市科技计划项目(No.201804010088);广东省普通高校特色创新类项目(No.2020KTSCX093)。

摘　　要：有限群G的子群H称为G的c-可补子群(c-正规子群),如果存在G的子群(正规子群)N,使得G=NH且N∩H≤H_(G),这里H_(G)=∩_(g∈G) H^(g)是H在G中的核.每个子群都c-可补(c-正规)的有限群称为有限c-可补群(CN-群).本文研究有限CN-群与有限c-可补群,获得了CN-群与c-可补群的一些新的结果.特别地,在方法上有一定的创新,完善近期关于CN-群的研究.A subgroup H of finite group G is called a c-supplemented subgroup(c-normal subgroup)of G if there exists a subgroup(normal subgroup)N such that G=NH and N∩H≤H_(G),where H_(G)=∩_(g∈G) H^(g) is the core of H in G.A finite group with every subgroup c-supplemented(c-normal)is called a finite c-supplemented group(CN-group).In this paper,many new characterizations of c-supplemented group were obtained.In particular,some methodological innovations have been made to improve the studies of the CN-group.

关 键 词：有限群 C-正规子群 CN-群 C-可补子群 c-可补群 

分 类 号：O152.2[理学—数学]