2019
Том 71
№ 2

# Kurdachenko L. A.

Articles: 22
Article (Russian)

### On some groups all subgroups of which are nearly pronormal

Ukr. Mat. Zh. - 2007. - 59, № 10. - pp. 1331–1338

A subgroup $H$ of a group $G$ is said to be nearly pronormal in $G$ if, for each subgroup $L$ of the group $G$ including H, the normalizer $N_L ( H)$ is contranormal in $L$. We prove that if $G$ is a (generalized) soluble group in which every subgroup is nearly pronormal, then all subgroups of $G$ are pronormal.

Article (Russian)

### Groups with weak maximality condition for nonnilpotent subgroups

Ukr. Mat. Zh. - 2006. - 58, № 8. - pp. 1068–1083

A group $G$ satisfies the weak maximality condition for nonnilpotent subgroups or, shortly, the condition Wmax-(non-nil), if $G$does not possess the infinite ascending chains $\{H_n | n \in N\}$ of nonnilpotent subgroups such that the indexes $|H_{n+i} :\; H_n |$ are infinite for all $n \in N$. In the present paper, we study the structure of hypercentral groups satisfying the weak maximality condition for nonnilpotent subgroups.

Article (Russian)

### Linear groups with minimality condition for some infinite-dimensional subgroups

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1476–1489

Let $F$ be a field, let $A$ be a vector space over $F$, and let $GL(F, A)$ be the group of all automorphisms of the space $A$. If $H$ is a subgroup of $GL(F, A)$, then we set aug $\dim_F (H) = \dim_F (A(ωFH))$, where $ωFH$ is the augmentation ideal of the group ring $FH$. The number ${\rm{aug} \dim}_F (H)$ is called the augmentation dimension of the subgroup $H$. In the present paper, we study locally solvable linear groups with minimality condition for subgroups of infinite augmentation dimension.

Article (Russian)

### Groups with Hypercyclic Proper Quotient Groups

Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 470-478

We continue the investigation of (solvable) groups all proper subgroups of which are hypercyclic. The monolithic case is studied completely; in the nonmonolithic case, however, one should impose certain additional conditions. We investigate groups all proper quotient groups of which possess supersolvable classes of conjugate elements.

Article (Russian)

### Modules over Group Rings with Certain Finiteness Conditions

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 931-940

We study modules over the group ring DG all proper submodules of which are finitely generated as D-modules.

Article (English)

### Groups with Bounded Chernikov Conjugate Classes of Elements

Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 798-807

We consider BCC-groups, that is groups G with Chernikov conjugacy classes in which for every element xG the minimax rank of the divisible part of the Chernikov group G/C G(x G) and the order of the corresponding factor-group are bounded in terms of G only. We prove that a BCC-group has a Chernikov derived subgroup. This fact extends the well-known result due to B. H. Neumann characterizing groups with bounded finite conjugacy classes (BFC-groups).

Article (Russian)

### Groups all proper quotient groups of which have Chernikov conjugacy classes

Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 346-353

We study groups all proper quotient groups of which are CC-groups.

Brief Communications (Ukrainian)

### On complementability of certain generalized hypercenters in Artinian modules

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1548–1552

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.

Article (Ukrainian)

### Groups with maximum condition for nonabelian subgroups

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 925–930

Article (Ukrainian)

### Groups with a dense system of infinite almost normal subgroups

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 969–973

Article (Ukrainian)

### Groups with minimax factor groups

Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 620–625

Article (Ukrainian)

### Locally nilpotent groups with the min ? ∞ ? n

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 340-346

Article (Ukrainian)

### Groups with weak minimality and maximality conditions for subgroups which are not normal

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1705–1709

Article (Ukrainian)

### Groups rich with almost-normal subgroups

Ukr. Mat. Zh. - 1988. - 40, № 3. - pp. 326-330

Article (Ukrainian)

### Two-step nilpotent FC-groups

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 329–335

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

Article (Ukrainian)

### Groups with noncyclic subgroups of finite index

Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 435—440

Article (Ukrainian)

### FC-groups with bounded periodic part

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 374 — 378

Article (Ukrainian)

### Groups with a complete system of almost-normal subgroups

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 42—46

Article (Ukrainian)

### Infinite groups with a generalized dense system of subnormal subgroups

Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 407–410

Article (Ukrainian)

### Nonperiodic groups with bounds for layers of elements

Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 386–389