# 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

Roiter A. V., Sergeychuk V. V.

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

It is proved that a finitely spaced module over $k$-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).

### Tame and wild subspace problems

Gabriel Р., Nazarova L. A., Roiter A. V., Sergeychuk V. V., Vossieck D.

Ukr. Mat. Zh. - 1993. - 45, № 3. - pp. 313–352

Assume that $B$ is a finite-dimensional algebra over an algebraically closed field $k$, $B_d = \text{Spec} k[B_d]$ is the affine algebraic scheme whose $R$-points are the $B ⊗_k k[B_d]$-module structures on $R^d$, and $M_d$ is a canonical $B ⊗_k k[B_d]$-module supported by $k[Bd^]d$. Further, say that an affine subscheme $Ν$ of $B_d$ isclass true if the functor $F_{gn} ∶ X → M_d ⊗_{k[B]} X$ induces an injection between the sets of isomorphism classes of indecomposable finite-dimensional modules over $k[Ν]$ and $B$. If $B_d$ contains a class-true plane for some $d$, then the schemes $B_e$ contain class-true subschemes of arbitrary dimensions. Otherwise, each $B_d$ contains a finite number of classtrue puncture straight lines $L(d, i)$ such that for eachn, almost each indecomposable $B$-module of dimensionn is isomorphic to some $F_{L(d, i)} (X)$; furthermore, $F_{L(d, i)} (X)$ is not isomorphic to $F_{L(l, j)} (Y)$ if $(d, i) ≠ (l, j)$ and $X ≠ 0$. The proof uses a reduction to subspace problems, for which an inductive algorithm permits us to prove corresponding statements.

### 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