The main problem of the theory of phenomenologically symmetric geometries of two sets is that of classification of these geometries. In this paper, by means of complexification by associative hypercomplex numbers, for functions of a pair of points of some known phenomenologically symmetric geometries of two sets (PhS GTS), we find functions of a pair of points of new geometries. We also find the equations of the groups of motions and establish the phenomenological symmetry of these geometries, i. e., find functional relations between functions of a pair of points for definite finite number of arbitrary points. In particular, for single-component functions of a pair of points of PhS GTS’s of rank (n, n) and (n + 1, n), we define s-component metric functions of a pair of points of the same rank and find the corresponding equations of the groups of motions and the equations which express their phenomenological symmetry.

中文翻译：

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两组某些几何中的超复数。II

两组现象学对称几何理论的主要问题是这些几何的分类问题。在本文中，通过关联超复数的复合化，对于某些已知的现象对称的两组几何（PhS GTS）的一对点的函数，我们找到了新几何的一对点的函数。我们还找到运动组的方程，并建立这些几何形状的现象学对称性，即，对于任意数量的有限点，找到一对点的函数之间的函数关系。特别是，对于排名为（n，n）和（n + 1，n）的PhS GTS的一对点的单分量函数，我们定义s对具有相同等级的一对点的分量度量函数，并找到运动组的相应方程式和表示其现象学对称性的方程式。