Sushchanskii V. I.
Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1299-1308
The notions of periodically defined and residual periodically defined linear transformations of an infinitedimensional vector space $V$ over the field $K$ are introduced. A group of all strictly residual periodically defined transformations and its subgroups of $u$-periodically defined transformations (where $u$ is a supernatural number) are investigated. A continual family of simple groups obtained as infinite-dimensional analogs of $PSL_n (K)$ is constructed.
Ukr. Mat. Zh. - 2010. - 62, № 11. - pp. 1500–1510
We characterize natural categories in which morphisms are defined by partial automata of the following three types: asynchronous automata, window automata, and automata synchronous over finite alphabets. We distinguish subcategories whose morphisms are defined by finite automata.
Lattice of normal subgroups of a group of local isometries of the boundary of a spherically homogeneous tree
Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1350–1356
We describe the structure of the lattice of normal subgroups of the group of local isometries of the boundary of a spherically homogeneous tree LIsom ∂T. It is proved that every normal subgroup of this group contains its commutant. We characterize the quotient group of the group LIsom ∂T by its commutant.
Second international Algebraic Conference in Ukraine dedicated to the memory of Professor L. A. Kaluzhnin
Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 574-576
Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1148–1155
Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 1031–1038
Structure of Sylow 2-subgroups of the alternating groups and normalizers of Sylow subgroups in the symmetric and alternating groups
Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 304–312