http://dspace.nbuv.gov.ua:80/handle/123456789/150377 2026-04-18T03:31:30Z 2026-04-18T03:31:30Z http://dspace.nbuv.gov.ua:80/handle/123456789/158443 2019-09-01T22:25:38Z 2013-01-01T00:00:00Z

Rostislav I . Grigorchuk. To the 60th anniversary On February 23, 2013, an outstanding mathematician, one of the founders of our journal Professor Rostislav I. Grigorchuk turns his 60th. The influence of Grigorchuk's famous results on the development of various branches of mathematics is difficult to overestimate and his active involvement in the international mathematics community life is pretty significant.

2013-01-01T00:00:00Z Plonka, E. http://dspace.nbuv.gov.ua:80/handle/123456789/152265 2019-06-09T22:25:19Z 2013-01-01T00:00:00Z

Associative words in the symmetric group of degree three Plonka, E. Let G be a group. An element w(x, y) of the absolutely free group on free generators x, y is called an associative word in G if the equality w(w(g₁, g₂), g₃)=w(g₁, w(g₂, g₃)) holds for all g₁, g₂ ∈ G. In this paper we determine all associative words in the symmetric group on three letters.

2013-01-01T00:00:00Z Pinedo, H. http://dspace.nbuv.gov.ua:80/handle/123456789/152264 2019-06-09T22:25:53Z 2013-01-01T00:00:00Z

On elementary domains of partial projective representations of groups Pinedo, H. We characterize the finite groups containing only elementary domains of factor sets of partial projective representations. A condition for a finite subset A of a group G, which contains the unity of the group, to induce an elementary partial representation, of G whose (idempotent) factor set is total is given. Finally, we characterize the elementary partial representation of abelian groups of degrees ≤ 4 with total factor set.

2013-01-01T00:00:00Z Oliynyk, B. http://dspace.nbuv.gov.ua:80/handle/123456789/152263 2019-06-09T22:25:39Z 2013-01-01T00:00:00Z

Infinitely iterated wreath products of metric spaces Oliynyk, B. The construction of the finitary wreath product of metric spaces and its completion, the infinitely iterated wreath product of metric spaces are introduced. They full isometry groups are described. Some properties and examples of these constructions are considered.

2013-01-01T00:00:00Z