We construct a 2-generated 2-related group without non-trivial finite factors-groups. This answers a question of J. Button.

A regular connected graph Γ of degree s is called kaleidoscopical if there is a (s + 1)-coloring of the set of its vertices such that every unit ball in Γ has no distinct monochrome points. The kaleidoscopical graphs can ...

In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones ...

Classification of the groups of local isometries of the rooted tree boundaries is established for transitive groups.

A ring R is filial when for every I, J, if I is an ideal of J and J is an ideal of R then I is an ideal of R. Several characterizations and results on structure of commutative reduced filial rings are obtained.

This is a survey paper on the distribution of arithmetical functions on some subsets of integers. Continuous homomorphisms as arithmetical functions, and sets of uniqueness are also treated.

In this paper, we introduce filtered and graded Procesi extensions of filtered and graded rings as a natural modification of Procesi extensions of rings. We show that these extensions behave well from the geometric point of view.

A semigroup S is called F- semigroup if there exists a group-congruence ρ on S such that every ρ-class contains a greatest element with respect to the natural partial order ≤S of S (see [8]). This generalizes the concept ...

The structure of groups whose non-normal subgroups have a finite commutator subgroup is investigated. In particular, it is proved that if k is a positive integer and G is a locally graded group in which every non-normal ...