http://dspace.nbuv.gov.ua:80/handle/123456789/150341 2026-04-18T12:14:38Z http://dspace.nbuv.gov.ua:80/handle/123456789/157378 Isolated and nilpotent subsemigroups in the variants of ISn Tsyaputa, G. All isolated, completely isolated, and nilpotent subsemigroups in the semigroup ISn of all injective partial transformations of an n-element set, considered as a semigroup with a sandwich multiplication are described. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157374 Isomorphisms of Cayley graphs of surface groups Bozejko, M.; Dykema, K.; Lehner, F. A combinatorial proof is given for the fact that the Cayley graph of the fundamental group Γg of the closed, orientable surface of genus g ≥ 2 with respect to the usual generating set is isomorphic to the Cayley graph of a certain Coxeter group generated by 4g elements. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157373 Strongly orthogonal and uniformly orthogonal many-placed operations Belyavskaya, G.; Mullen, G.L. In [3] we have studied connection between orthogonal hypercubes and many-placed (d-ary) operations, have considered different types of orthogonality and their relationships. In this article we continue study of orthogonality of many-placed operations, considering special types of orthogonality such as strongly orthogonality and uniformly orthogonality. We introduce distinct types of strongly orthogonal sets and of uniformly orthogonal sets of d-ary operations, consider their properties and establish connections between them. 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/157370 Uncountably many non-isomorphic nilpotent real n-Lie algebras Stitzinger, E.; Williams, M.P. There are an uncountable number of non-isomorphic nilpotent real Lie algebras for every dimension greater than or equal to 7. We extend an old technique, which applies to Lie algebras of dimension greater than or equal to 10, to find corresponding results for n-Lie algebras. In particular, for n ≥ 6, there are an uncountable number of non-isomorphic nilpotent real n-Lie algebras of dimension n + 4. 2006-01-01T00:00:00Z