http://dspace.nbuv.gov.ua:80/handle/123456789/150354 Wed, 22 Apr 2026 13:14:13 GMT 2026-04-22T13:14:13Z http://dspace.nbuv.gov.ua:80/bitstream/id/448100/ http://dspace.nbuv.gov.ua:80/handle/123456789/150354 http://dspace.nbuv.gov.ua:80/handle/123456789/153373 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. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/153373 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153366 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). Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/153366 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153365 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. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/153365 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153364 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. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/153364 2008-01-01T00:00:00Z