Algebra and Discrete Mathematics, 2008, № 2 http://dspace.nbuv.gov.ua:80/handle/123456789/150353 2022-10-06T18:04:12Z 2022-10-06T18:04:12Z Emmanuil Moiseevich Zhmud’ (1918-2007) Favorov, S. Novikov, B. Vyshnevetskiy, A. Zholtkevich, G. http://dspace.nbuv.gov.ua:80/handle/123456789/153371 2019-06-14T22:25:43Z 2008-01-01T00:00:00Z Emmanuil Moiseevich Zhmud’ (1918-2007) Favorov, S.; Novikov, B.; Vyshnevetskiy, A.; Zholtkevich, G. 2008-01-01T00:00:00Z Random walks on finite groups converging after finite number of steps Vyshnevetskiy, A.L. Zhmud, E.M. http://dspace.nbuv.gov.ua:80/handle/123456789/153370 2019-06-14T22:25:43Z 2008-01-01T00:00:00Z Random walks on finite groups converging after finite number of steps Vyshnevetskiy, A.L.; Zhmud, E.M. Let P be a probability on a finite group G, P(n)=P∗…∗P (n times) be an n-fold convolution of P. If n→∞, then under mild conditions P(n) converges to the uniform probability U(g)=1|G| (g∈G). We study the case when the sequence P(n) reaches its limit U after finite number of steps: P(k)=P(k+1)=⋯=U for some k. Let Ω(G) be a set of the probabilities satisfying to that condition. Obviously, U∈Ω(G). We prove that Ω(G)≠U for ``almost all'' non-Abelian groups and describe the groups for which Ω(G)=U. If P∈Ω(G), then P(b)=U, where b is the maximal degree of irreducible complex representations of the group G. 2008-01-01T00:00:00Z On τ-closed totally saturated group formations with Boolean sublattices Safonov, V.G. http://dspace.nbuv.gov.ua:80/handle/123456789/153363 2019-06-14T22:25:39Z 2008-01-01T00:00:00Z On τ-closed totally saturated group formations with Boolean sublattices Safonov, V.G. In the universe of finite groups the description of τ-closed totally saturated formations with Boolean sublattices of τ-closed totally saturated subformations is obtained. Thus, we give a solution of Question 4.3.16 proposed by A.N.Skiba in his monograph "Algebra of Formations" (1997). 2008-01-01T00:00:00Z Balleans of bounded geometry and G-spaces Protasov, I.V. http://dspace.nbuv.gov.ua:80/handle/123456789/153361 2019-06-14T22:25:42Z 2008-01-01T00:00:00Z Balleans of bounded geometry and G-spaces Protasov, I.V. A ballean (or a coarse structure) is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that a ballean can be considered as an asymptotical counterpart of a uniform topological space. We prove that every ballean of bounded geometry is coarsely equivalent to a ballean on some set X determined by some group of permutations of X. 2008-01-01T00:00:00Z