2019
Том 71
№ 11

Tushev A. V.

Articles: 11
Article (Ukrainian)

Induced Representations of Abelian Groups of Finite Rank

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1249-1253

We prove that any irreducible faithful representation of an almost torsion-free Abelian group G of finite rank over a finitely generated field of characteristic zero is induced from an irreducible representation of a finitely generated subgroup of the group G.

Article (Russian)

On Solvable Groups with Proper Quotient Groups of Finite Rank

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1560-1568

We study solvable groups of infinite special rank all proper normal subgroups of which define quotient groups of finite special rank.

Article (Russian)

On Noetherian Modules over Minimax Abelian Groups

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 969-980

We consider modules over minimax Abelian groups. We prove that if A is an Abelian minimax subgroup of the multiplicative group of a field k and if the subring K of the field k generated by the subgroup A is Noetherian, then the subgroup A is the direct product of a periodic group and a finitely generated group.

Brief Communications (Russian)

On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 571-572

In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of $A$ that maps $x,y$ into $a_x, b_y$, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”

Article (Russian)

On exact irreducible representations of locally normal groups

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1688–1694

We obtain a generalization of the Gaschutz criterion of existence of exact irreducible representations of finite groups to the class of normal groups.

Article (Russian)

On solvable groups, all proper factor groups of which have finite ranks

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1274–1281

This paper deals with finitely generated finitely approximable solvable groups of infinite special rank, all proper normal subgroups of which determine the factor groups of finite special ranks.

Article (Ukrainian)

Noether modules over abelian groups of finite free rank

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 1042–1048

Article (Ukrainian)

Irreducible representations of locally polycyclic groups over an absolute field

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1389–1394

Article (Ukrainian)

Condition min-?-N and the representations of solvable groups connected with IT

Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 677–681

Article (Ukrainian)

Some classes of groups with weak minimal condition for normal subgroups

Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 457–462

Article (Ukrainian)

Two-step solvable groups with weak minimal condition for normal subgroups

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 300–306