2019
Том 71
№ 11

# Bodnarchuk Yu. V.

Articles: 6
Article (Ukrainian)

### Locally nilpotent derivations and Nagata-type utomorphisms of a polynomial algebra

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1011-1024

We study locally nilpotent derivations belonging to a Lie algebra $sa_n$ of a special affine Cremona group in connection with the root decompositions of sa n relative to the maximum standard torus. It is proved that all root locally nilpotent derivations are elementary. As a continuation of this research, we describe two- and three-root derivations. By using the results obtained by Shestakov and Umirbaev, it is shown that the exponents of almost all obtained three-root derivations are wild automorphisms of a polynomial algebra in three variables.

Brief Communications (Ukrainian)

### On the endomorphisms of translation modules of polynomials

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 277-281

We determine the structure of a ring of endomorphisms of a translation module whose structure is determined by a group of translations of an affine space that acts by means of displacement on a polynomial algebra.

Article (Russian)

### On the isomorphism of wreath products of groups

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 671–679

The well-known Neumann theorem on the isomorphism of standard wreath products is generalized to the wreath products of an arbitrary transitive permutation group and an abstract group.

Article (Ukrainian)

### Automorphisms of multiple wreath products of abelian p-groups

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 889–894

Article (Ukrainian)

### Structure of the group of automorphisms of a Sylow p-subgroup of the symmetric group S p n (p ≠ 2)

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 688 – 694

Article (Ukrainian)

### Structure of the automorphism group of a nonstandard wreath product

Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 143 - 148