http://dspace.nbuv.gov.ua:80/handle/123456789/150372 2026-04-20T12:49:25Z http://dspace.nbuv.gov.ua:80/handle/123456789/158439 D. I . Zaitsev In the spring of 2012, the 70th birthday of Dmitriy I. Zaitsev (1942-1990) will come. D.I Zaitsev did not live two years to his 50th birthday, but his life in mathematics will be long. His main interests were very wide; they spread over all areas of modern group theory. His work greatly influenced the development of the infinite group theory. Many of his results have already become classical and have been included in monographs and surveys. The methods developed by him found numerous followers who have successfully applied them. 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152191 Finite local nearrings on metacyclic Miller-Moreno p-groups Raievska, I.Yu.; Sysak, Ya.P. In this paper the metacyclic Miller-Moreno p-groups which appear as the additive groups of finite local nearrings are classified. 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152190 Partitions of groups into sparse subsets Protasov, I. A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) sparse subsets. If |G| > (κ+)א0 then η(G) > κ, if |G| ≤ κ+ then η(G) ≤ κ. We show also that cov(A) ≥ cf|G| for each sparse subset A of an infinite group G, where cov(A) = min{|X| : G = X A}. 2012-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/152189 On hypercentral fyzzy groups Kurdachenko, L.A.; Grin, K.O.; Turbay, N.A. In an arbitrary fuzzy group we construct the upper central series and consider some its properties. In particular, the characterization of nilpotent fuzzy group has been obtained. 2012-01-01T00:00:00Z