A ring A is called an FDI-ring if there exists a decomposition of the identity of A in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent e artinian if the ring eAe is ...

Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some its subgroup D satisfying 1 <|D| < |P| and study the structure of G under assumption that all subgroups H of P with |H| = |D| are c-normal in G.

The results on automorphisms of homogeneous alternating groups are corrected and improved.

Let A, B be subgroups of a group G and ∅ 6= X ⊆ G. A subgroup A is said to be X-permutable with B if for some x ∈ X we have ABx = BxA. We obtain some new criterions for supersolubility of a finite group G = AB, where A ...

All H−,R− and L−cross-sections of the infinite symmetric inverse semigroup ISX are described.

V.I. Arnold gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to A, can be reduced by ...

The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions ...

Let G be a finite group and let = g2G g be a strongly G-graded R-algebra, where R is a commutative ring with unity. We prove that if R is a Dedekind domain with quotient field K, is an R-order in a separable K-algebra ...

General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical ...

We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies on the infinite semigroup of matrix units B such that (B , ) is a semitopological (inverse) semigroup are ...