2^3p阶群的一组最简生成元集的Cayley图

On Cayley Graph of 2^3p Order-graphs of a Simple Generic Set

I.格罗斯曼和W.迈格努斯在“群和它的图象表示”中给出了群的几何图象——群的Cayley图.主要是通过正多边形和正多面体的重合运动求群的Cayley图,它适合于求点群的Cayley图.本文主要给出了由群的定义关系较复杂的有限群来直接求群的Cayley图的方法,揭示了其结构规律性和自身特点,并通过两个群元素的乘法对应于图象上的两个相继的道路合成给出了理论证明.从而丰富了“群和它的图象表示”所创立群的Cayley图的理论.最后给出了23p阶群的Cayley图.

I. Grossmaan and W. Magnus proposed the geometric figure, i.e. the Cayley graphs of groups in the figure representation of groups. We get Cayley graphs of groups mostly through the coincident motion of regular polygon and regular polyhedron, it is suitable to find Cayley graphs of groups of a point. In this paper, it is shown that how to get the Cayley graphs of groups by the finite groups defined complicated and the theoretical prove is given by the coincident rule of critical paths. Thereby the theory of Cayley graphs of groups in the figure representation of groups is enriched. The last Cayley graphs of 2^3P order-groups are presented as examples of application.