| 元素的阶与幂零群的刻画 |
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| 引用本文： | 沈如林.元素的阶与幂零群的刻画[J].湖北民族学院学报(哲学社会科学版),2009,27(3). |
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| 作者姓名： | 沈如林 |
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| 作者单位： | 湖北民族学院数学系,湖北恩施,445000 |
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| 基金项目： | 国家自然科学基金，湖北省教育厅重点项目 |
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| 摘 要： | 给出了幂零群及交换群的一个等价刻画,证明了若有限群G是交换(幂零)群当且仅当G的相同(互素)的素幂阶元素交换.
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| 关 键 词： | 幂零群 交换群 内幂零群 内交换群 |
Orders of Elements and Characterization of Finite Nilpotent Groups |
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| SHEN Ru-lin.Orders of Elements and Characterization of Finite Nilpotent Groups[J].Journal of Hubei Institute for Nationalities(Natural Sciences),2009,27(3). |
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| Authors: | SHEN Ru-lin |
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| Institution: | Department of Mathematics;Hubei University for Nationalities;Enshi 445000;China |
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| Abstract: | In this paper we give characterizations of finite nilpotent and abelian groups.It is proven that a finite group is abelian(resp.nilpotent) if and only if elements of the same(resp.coprime) order with prime power are commutative. |
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| Keywords: | nilpotent groups abelian groups inner nilpotent groups inner abelian groups |
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