有限CN-群与有限c-可补群

On Finite CN-Groups and Finite c-Supplemented Groups

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.