| 有限CN-p-群 |
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| 引用本文： | 石化国,韩章家,郭鹏飞,张隆辉.有限CN-p-群[J].数学学报,2019,62(2):211-218. |
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| 作者姓名： | 石化国 韩章家 郭鹏飞 张隆辉 |
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| 作者单位： | 1. 四川职业技术学院应用数学与经济系 遂宁 629000;
2. 成都信息工程大学应用数学学院 成都 610225;
3. 海南师范大学数学与统计学院 海口 571158;
4. 四川职业技术学院学报编辑部 遂宁 629000 |
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| 基金项目： | 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） |
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| 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.
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| 关 键 词： | 有限群 C正规子群 CN-p群 幂自同构 |
On Finite CN-p-groups |
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| Hua Guo SHI,Zhang Jia HAN,Peng Fei GUO,Long Hui ZHANG.On Finite CN-p-groups[J].Acta Mathematica Sinica,2019,62(2):211-218. |
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| Authors: | Hua Guo SHI Zhang Jia HAN Peng Fei GUO Long Hui ZHANG |
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| Institution: | 1. Department of Applied Mathematics and Economics, Sichuan Vocational and Technical College, Suining 629000, P. R. China;
2. School of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P. R. China;
3. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China;
4. Journal Editorial Office of Sichuan, Vocational and Technical College, Suining 629000, P. R. China |
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| Abstract: | 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. |
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| Keywords: | finite group C-normal subgroup CN-p-group power automorphism |
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