http://dspace.nbuv.gov.ua:80/handle/123456789/150354 2026-04-22T13:14:24Z 2026-04-22T13:14:24Z Banakh, T.T. Gavrylkiv, V. Nykyforchyn, O. http://dspace.nbuv.gov.ua:80/handle/123456789/153373 2019-06-14T22:25:44Z 2008-01-01T00:00:00Z

Algebra in superextensions of groups, I: zeros and commutativity Banakh, T.T.; Gavrylkiv, V.; Nykyforchyn, O. Given a group X we study the algebraic structure of its superextension λ(X). This is a right-topological semigroup consisting of all maximal linked systems on X endowed with the operation A∘B={C⊂X:{x∈X:x−1C∈B}∈A} that extends the group operation of X. We characterize right zeros of λ(X) as invariant maximal linked systems on X and prove that λ(X) has a right zero if and only if each element of X has odd order. On the other hand, the semigroup λ(X) contains a left zero if and only if it contains a zero if and only if X has odd order |X|≤5. The semigroup λ(X) is commutative if and only if |X|≤4. We finish the paper with a complete description of the algebraic structure of the semigroups λ(X) for all groups X of cardinality |X|≤5.

2008-01-01T00:00:00Z Safonov, V.G. http://dspace.nbuv.gov.ua:80/handle/123456789/153366 2019-06-14T22:26:28Z 2008-01-01T00:00:00Z

On a question of A. N. Skiba about totally saturated formations Safonov, V.G. It is proved that the lattice of τ-closed totally saturated formations of finite groups is distributive. This is a solution of Question 4.2.15 proposed by A. N. Skiba in his monograph "Algebra of Formations" (1997).

2008-01-01T00:00:00Z Laurincikas, A. Macaitiene, R. http://dspace.nbuv.gov.ua:80/handle/123456789/153365 2019-06-14T22:25:38Z 2008-01-01T00:00:00Z

Discrete limit theorems for Estermann zeta-functions. II Laurincikas, A.; Macaitiene, R. A discrete limit theorem in the sense of weak convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function with explicitly given the limit measure is proved.

2008-01-01T00:00:00Z Woryna, A. http://dspace.nbuv.gov.ua:80/handle/123456789/153364 2019-06-14T22:26:23Z 2008-01-01T00:00:00Z

The generalized dihedral groups Dih(Zn) as groups generated by time-varying automata Woryna, A. Let Zn be a cubical lattice in the Euclidean space Rn. The generalized dihedral group Dih(Zn) is a topologically discrete group of isometries of Zn generated by translations and reflections in all points from Zn. We study this group as a group generated by a (2n+2)-state time-varying automaton over the changing alphabet. The corresponding action on the set of words is described.

2008-01-01T00:00:00Z