Statistical Destribution on Symmetry Groups

群论成功地应用于晶体结构的分析。晶体物质的对称性由32个点群中的一个来表示。本文介绍了晶体物质在32个点群中的分布的随机模型。考虑一个点群x，并采取可能的对称操作。可以随机加到x上。假设操作次数由泊松分布给出。将这些操作加到x上，得到由这些操作和x产生的点群。利用该模型进行了模拟研究，并将结果与晶体物质分布数据进行了比较。

Group theory is successfully applied to analysis of crystal structure. The symmetry of a crystalline substance is represented by one of the 32 point groups In this note a stochastic model is introduced for the distribution of crystalline substances among the 32 point groups. Consider a point group x. and take possible symmetry operations.which can be added to the x. at random. Assume the number of operations is given by Poisson distribution. Add the operations to the x and we get a point group generated by the operations and the x. A simulation study is carried out by the model to compave the result with the data of the distribution of crystalline substances.