| 正多边形对称群的子群 |
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| 引用本文： | 顾艳红.正多边形对称群的子群[J].纯粹数学与应用数学,2011,27(2):236-239. |
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| 作者姓名： | 顾艳红 |
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| 作者单位： | 北京林业大学理学院; |
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| 基金项目： | 中央高校基本科研业务费专项资金 |
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| 摘 要： | 利用Lagrange定理和正多边形对称群的性质,首先对正多边形对称群的子群的性质进行了研究,其次讨论了正多边形对称群的子群的结构,由此完全确定了正多边形对称群的子群,最后应用所得结论求出了正六边形对称群的所有子群.
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| 关 键 词： | 正多边形 群 对称群 子群 |
The subgroups of regular polygons symmetry group |
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| GU Yan-hong.The subgroups of regular polygons symmetry group[J].Pure and Applied Mathematics,2011,27(2):236-239. |
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| Authors: | GU Yan-hong |
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| Institution: | GU Yan-hong(College of Science,Beijing Forestry University,Beijing 100083,China) |
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| Abstract: | Utilizing the Lagrange theorem and the properties of regular polygons symmetry group,the properties of the subgroups of regular polygons symmetry group are studied.Then the structure of the subgroups of regular polygons symmetry group are obtained.Therefore,all the subgroups of regular polygons symmetry group are completely determined.Finally,an example about regular hexagon symmetry group is used to illuminate how to ascertain its subgroups. |
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| Keywords: | regular polygons group symmetry group subgroup |
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