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PDF(442 KB)
PDF(442 KB)
有限CN-p-群
On Finite CN-p-groups
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CN-p-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），ga=g或者对任意g ∈ Φ（G），ga=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.
有限群 / C-正规子群 / CN-p-群 / 幂自同构 {{custom_keyword}} /
finite group / C-normal subgroup / CN-p-group / power automorphism {{custom_keyword}} /
[1] Li C., Wang Y., Xie Z., Su N., Finite groups in which every subgroup is c-normal (in Chinese), Science in China: Mathematics, 2013, 43(1): 25–32.
[2] Miller G. A., Moreno H. C., Non-Abelian groups in which every subgroup is abelian, Trans. Amer Math. Soc., 1903, 4: 398–404.
[3] Robinson D. J. S., A Course in the Theory of Groups, Springer, New York, 1993.
[4] Wang L., The in uence of permutable properties of subgroups on the structure of finite groups (in Chinese), PH.D. Thesis of Zhongshan University, Guangzhou, 2006.
[5] Wang Y., C-normality of groups and its properties, J. Algebra, 1996, 180(3): 954–965.
[6] Xu M., An Introduction to Finite Groups Vol. 1(2nd Edition) (in Chinese), Science Publishing, Beijing, 2001.
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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