2019
Том 71
№ 6

# Tushev A. V.

Articles: 10
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 (Ukrainian)

### 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 (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