ЛИНЕЙНЫЕ ТОЧЕЧНЫЕ ГРУППЫ СИММЕТРИИ КЛАССИЧЕСКИХ И n – МЕРНЫХ ЭВКЛИДОВЫХ ПРОСТРАНСТВ ПРИ n ≥ 4

Abstract

In articol autorul face o sinteză a rezultatelor privind generalizarea grupurilor liniare punctuale unidimensionale G10 de antisimetrie simplă şi l-multiplă, cu P–simetrii de rozete, tablete, hipertablete, cristalografice, hipercristalografice şi birozete. Sunt descrise o serie de probleme ce pot fi rezolvate cu ajutorul grupurilor P G210 şi P G20 din P – simetriile de simetrii ce se conţin în categoriile noi ale spaţiilor euclidiene dimensionale 4 ≤ n ≤ 7.

One-dimensional point groups G10 were generalized with the simple and l–fold antysymmetry, also with the rosetal, tabletal, hypertabletal, crystallographic, hipercrystallographic and birossetal P–symmetries. The number of the lineal point symmetry groups of classical spaces was proved and the number of the lineal point groups of the n – dimensional spaces (when 4 ≤ n ≤ 7) was put by means of the obtained groups P G10 of the remarked particular cases of the P–symmetry.