摘要
每个子群都C-正规的有限群称为CN-群.本文首先给出二元生成的CN-p-群的完全分类.在此基础上得到CN-p-群的结构:当p为奇素数时,有限群G为CNp-群当且仅当G的每个元都平凡地作用在Φ(G)上;有限群G为CN-2-群当且仅当对任意给定的a∈G,都有对任意g∈Φ(G),g^a=g或者对任意g∈Φ(G),g^a=g^(-1).最后给出两个CN-p-群的直积是CN-p-群的判定条件.
A finite group G is called a CN-group if every subgroup H of G is C-normal in G. In this paper, we will give first a complete classification of the 2-generator CN-p-groups. Then by applying the structure of the 2-generator CN-p-groups, we obtain the following results: If p is a odd prime, then G is a CN-p-group if and only if Φ(G) ≤ Z(G). If p = 2, then G is a CN-p-group if and only if for any given a ∈G and for any g ∈ Φ(G), we have ga =g or ga = g^-1. We also get some criteria of CN-p-groups in terms of direct product of CN-p-groups.
作者
石化国
韩章家
郭鹏飞
张隆辉
Hua Guo SHI;Zhang Jia HAN;Peng Fei GUO;Long Hui ZHANG(Department of Applied Mathematics and Economics, Sichuan Vocational and Technical College,Suining 629000,P.R.China;School of Applied Mathematzcs,Chengdu University of Information Technology, Chengdu 610225,P.R.China;School of Mathematics and Statistics,Hainan Normal University, Haikou 571158,P.R.China;Journal Editorial Office of Sichuan,Vocational and Technical College, Suining 629000,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2019年第2期211-218,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(11661031)
四川省教育厅科学研究基金资助项目(18ZA0434)
关键词
有限群
C正规子群
CN-p群
幂自同构
finite group
C-normal subgroup
CN-p-group
power automorphism
