# Sergeychuk V. V.

### Topological Classification of the Oriented Cycles of Linear Mappings

Rybalkina T. V., Sergeychuk V. V.

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1407–1413

We consider oriented cycles of linear mappings over the fields of real and complex numbers. the problem of their classification to within the homeomorphisms of spaces is reduced to the problem of classification of linear operators to within the homeomorphisms of spaces studied by N. Kuiper and J. Robbin in 1973.

### On subgroups lifting modulo central commutant

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 742–745

We consider a finitely generated group *G* with the commutant of odd order \(p_1^{n_1 } \ldots p_s^{n_s } \) located at the center and prove that there exists a decomposition of *G/G′* into the direct product of indecomposable cyclic groups such that each factor except at most *n* _{l} + ... + *n* _{s} factors lifts modulo commutant.

### Elementary and multielementary representations of vectroids

Belousov K. I., Nazarova L. A., Roiter A. V., Sergeychuk V. V.

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1451–1477

We prove that every finitely represented vectroid is determined, up to an isomorphism, by its completed biordered set. Elementary and multielementary representations of such vectroids (which play a central role for biinvolutive posets) are described.

### Existence of a multiplicative basis for a finitely spaced module over an aggregate

Rоіlеr А. V., Sergeychuk V. V.

Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 567–579

It is proved that a finitely spaced module over a*k*-category admits a multiplicative basis (such a module gives rise to a matrix problem in which the allowed column transformations are determined by a module structure, the row transformations are arbitrary, and the number of canonical matrices is finite).

### Classification of pairs of subspaces in scalar product spaces

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 549–554

### Finitely generated groups with commutator group of prime order

Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 789–796