http://dspace.nbuv.gov.ua:80/handle/123456789/150383 2026-04-09T14:14:32Z http://dspace.nbuv.gov.ua:80/handle/123456789/158467 Igor Volodymyrovych Protasov (dedicated to 60-th Birthday) 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153340 The algorithms that recognize Milnor laws and properties of these laws Tomaszewski, W. We consider several equivalent definitions of the so-called Milnor laws (or Milnor identities) that is the laws which are not satisfied in ApA varieties. The purpose of this article is to provide algorithms that allow us to check whether a given identity w(x, y) has one of the following properties: w(x, y) is a Milnor law, every nilpotent group satisfying w(x, y) is abelian, every finitely generated metabelian group satisfying w(x, y) is finite-by-abelian. 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153339 Non-commutative Grillet semigroups Novikov, B.V. Grillet semigroups are introduced. This class of semigroups contains regular semigroups and complete commutative semigroups (by Grillet’s terminology). Some structural theorems are proved. 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153338 Subpower Higson corona of a metric space Kucab, Ja.; Zarichnyi, M. We define a subpower Higson corona of a metric space. This corona turns out to be an intermediate corona between the Higson corona and sublinear Higson corona. It is proved that the subpower compactification of an unbounded proper metric space contains a topological copy of the Stone-Cech compactification of a countable discrete space. We also provide an example of a map between geodesic spaces that is not asymptotically Lipschitz but that generates a continuous map of the corresponding subpower Higson coronas. 2014-01-01T00:00:00Z