Derived norms of finite groups  

作　　者：Zhencai Shen Shirong Li Jiping Zhang 

机构地区：[1]College of Science,China Agricultural University,Beijing100183,China [2]Department of Mathematics,Guangxi University,Nanning 530004,China [3]LMAM and School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2022年第12期2493-2502,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11631001 and 12071181);。

摘　　要：The intersection of particular subgroups is a kind of interesting substructure in group theory. Let G be a finite group and D(G) be the intersection of the normalizers of the derived subgroups of all the subgroups of G. A group G is called a D-group if G = D(G). In this paper, we determine the nilpotency class of the nilpotent residual G^(N) and investigate the structure of D(G) by a new concept called the IO-D-group. A non-D-group G is called an IO-D-group(inner-outer-D-group) if all of its proper subgroups and proper quotient groups are D-groups. The structure of IO-D-groups are described in detail in this paper. As an application of the classification of IO-D-groups, we prove that G is a D-group if and only if any subgroup of G generated by3 elements is a D-group.

关 键 词：derived subgroups D-groups nilpotent residuals IO-D-groups 

分 类 号：O152.1[理学—数学]