Algebra and Discrete Mathematics, 2008, № 3http://dspace.nbuv.gov.ua:80/handle/123456789/1503542021-03-01T01:54:02Z2021-03-01T01:54:02ZAlgebra in superextensions of groups, I: zeros and commutativityBanakh, T.T.Gavrylkiv, V.Nykyforchyn, O.http://dspace.nbuv.gov.ua:80/handle/123456789/1533732019-06-14T22:25:44Z2008-01-01T00:00:00ZAlgebra 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.
2008-01-01T00:00:00ZOn a question of A. N. Skiba about totally saturated formationsSafonov, V.G.http://dspace.nbuv.gov.ua:80/handle/123456789/1533662019-06-14T22:26:28Z2008-01-01T00:00:00ZOn 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).
2008-01-01T00:00:00ZDiscrete limit theorems for Estermann zeta-functions. IILaurincikas, A.Macaitiene, R.http://dspace.nbuv.gov.ua:80/handle/123456789/1533652019-06-14T22:25:38Z2008-01-01T00:00:00ZDiscrete 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.
2008-01-01T00:00:00ZThe generalized dihedral groups Dih(Zn) as groups generated by time-varying automataWoryna, A.http://dspace.nbuv.gov.ua:80/handle/123456789/1533642019-06-14T22:26:23Z2008-01-01T00:00:00ZThe 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