恰有两个子群共轭类长的有限群

唐锋

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 619-622.

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数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 619-622. DOI: 10.12386/A2011sxxb0063
论文

恰有两个子群共轭类长的有限群

    唐锋
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Finite Groups with Exactly Two Conjugacy Class Sizes of Subgroups

    Feng TANG
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文章历史 +

摘要

设G是有限群, Ns(G)表示G的子群共轭类长构成的集合. 本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.  

Abstract

Let G be a finite group and Ns(G) denote the set of conjugacy class sizes of all subgroups of G. The aim of this paper is to investigate the finite groups G with Ns(G) exactly having two elements. We classfy the groups for the nonnilpotent case, and also obtain some properties for the nilpotent case.  

关键词

有限群 / 子群共轭类长 / Dedekind群

Key words

finite group / conjugacy class size of subgroup / Dedekind group

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唐锋. 恰有两个子群共轭类长的有限群. 数学学报, 2011, 54(4): 619-622 https://doi.org/10.12386/A2011sxxb0063
Feng TANG. Finite Groups with Exactly Two Conjugacy Class Sizes of Subgroups. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 619-622 https://doi.org/10.12386/A2011sxxb0063

参考文献

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基金

国家自然科学基金资助项目(10871032)

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