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.
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.
出处
《纯粹数学与应用数学》
CSCD
2011年第2期236-239,共4页
Pure and Applied Mathematics
基金
中央高校基本科研业务费专项资金
关键词
正多边形
群
对称群
子群
regular polygons
group
symmetry group
subgroup
