We characterize semigroups X whose semigroups of filters φ(X), maximal linked systems λ(X), linked upfamilies N₂(X), and upfamilies υ(X) are commutative.

In 1995 in Kourovka notebook the second author asked the following problem: is it true that for each partition G=A₁ ∪ ⋯ ∪ An of a group G there is a cell Ai of the partition such that G = FAiA⁻¹i for some set F ⊂ G of ...

Grillet semigroups are introduced. This class of semigroups contains regular semigroups and complete commutative semigroups (by Grillet’s terminology). Some structural theorems are proved.

The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group L = Z₂≀Z is a condensation group and has a minimal ...

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 ...

We prove that the elements of the Hanoi Towers groups Hm have depth bounded from above by a poly-logarithmic function O(logm⁻²n), where n is the length of an element. Therefore the word problem in groups Hm is solvable in ...