2018
Том 70
№ 11

All Issues

Bodnarchuk Yu. V.

Articles: 6
Article (Ukrainian)

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

Bodnarchuk Yu. V., Prokof’ev P. H.

↓ Abstract   |   Full text (.pdf)

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

Bodnarchuk Yu. V.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

On the isomorphism of wreath products of groups

Bodnarchuk Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Bodnarchuk Yu. V.

Full text (.pdf)

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)

Bodnarchuk Yu. V.

Full text (.pdf)

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

Article (Ukrainian)

Structure of the automorphism group of a nonstandard wreath product

Bodnarchuk Yu. V.

Full text (.pdf)

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