ИССЛЕДОВАНИЕ ПЯТИМЕРНЫХ ТОЧЕЧНЫХ ГРУПП СИММЕТРИИ С ИНВАРИАНТНОЙ ДВУМЕРНОЙ ПЛОСКОСТЬЮ И НЕПОДВИЖНОЙ ТОЧКОЙ НА НЕЙ

Александр ПАЛИСТРАНТ Кафедра алгебры и геометрии

Аннотация

At present in the Departmentof the Algebra and Geometry of the Moldavian State University an extensive research investigations of studying of the subperiodical subgroups of the five-dimensional Fedorov groups are conducted. In the studying process of a such subgroups it is important to know not only the number of symmetry groups, composing the considering category of the planar subgroups of the five-dimensional Fedorov groups, but also the structure of every certain group of the investigating category. In order to identify the structures of the five-dimensional point symmetry groups with an invariant two-dimensional plane and a fixed point on it, i. e. the symmetry groups of the category G520 in a brief notation as P G30, which up to structure are interpreted by 1208 two-dimensional point groups of the crystallographic P-symmetries for P G30, the detailed review of the catalog of all types of two-dimensional P-symmetry point groups, entering in the set of the 1208 two-dimensional point groups P C20 for P G30, is given.