INVESTGATION OF THE FIVE-DMENSIONAL SYMMETRY GROUPS WITH INVARIANT TWO-DIMENSIONAL PLANE, STRAIGHT LINE INTO IT AND A POINT ON THIS LINE

Александр ПАЛИСТРАНТ Молдавский государственный университет

Abstract

To identify the structure of the five-dimensional symmetry groups with invariant two-dimensional plane, straight line in it and a point on this line, that is, five-dimensional symmetry groups of the G5210 category in brief notation, the catalog of the two-dimensional groups of the crystallographic P-symmetries for P G30 is completely presented. It is proven that between the groups and five dimensional symmetry groups of the G5210 category established not only one to one, but also strongly isomorphic correspondence, which means that P-symmetry group of the category and modeled by this group the symmetry group of the category G5210 have the sa me structure. Keywords: five-dimensional symmetry groups, invariant two-dimensional plane, catalog the two-dimensional grups of the crystallographic P-symetries.