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Planar point groups of tablets and hypertablets $P$-symmetries and their application to the study of multidimensional symmetry groups. (Russian)
Authors: Palistrant A. F.
Abstract
The hyper-tablet $P$-symmetries are considered where the substitution group $P$ is isomorphic to a four-dimensional crystallographic point group with invariant three-dimensional and embedded in it two-dimensional planes (category $G_{4320}$). The full classification of middle groups of such $P$-symmetries is given and two-dimensional point groups $G_2{}_0^P$ for all 125 revealed hyper-tablet $P$-symmetries are counted. The groups obtained are applied to derive six-dimensional symmetry groups of category $G_{65420}$. Using groups $G_{320}$ of 31 tablet $P$-symmetries ($P \simeq G_{320}$) the correctness of resulting number 8806 of symmetry groups of category $G_{65420}$ is confirmed.Universitatea de Stat din Moldova
str. Mateevici 60, Chişinău MD-2009, Moldova
str. Mateevici 60, Chişinău MD-2009, Moldova
Contents
- Morita contexts and correspondences between lattices of submodules. (Russian)
- A theorem on union of $d$-star-shaped sets. (Russian)
- Planar point groups of tablets and hypertablets $P$-symmetries and their application to the study of multidimensional symmetry groups. (Russian)
- On the generalized Fibonacci sequence. (English)
- Idempotents and the radical with respect to a right ideal. II. (Russian)
- Concordant solutions of linear multidimensional differential equations. (Russian)
- On the completeness of topological modules free in some classes. (English)
- The principle of composition of multidimensional dynamical systems. (Russian)
- Algorithms of choice of optimal configurations in weighted digraphs. (Russian)
- The construction of a numerable collection of precomplete classes of formulae in the provability logic. (English)
- On the strong isomorphism of groups and isomorphism of $P$-symmetries. (Russian)
- Uniqueness of topologies in the case of some constructions of rings and modules. (Russian)
