2019
Том 71
№ 11

All Issues

Kurdachenko L. A.

Articles: 22
Article (Russian)

On some groups all subgroups of which are nearly pronormal

Kurdachenko L. A., Russo A., Vincenzi G.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Semko N. N.

↓ Abstract   |   Full text (.pdf)

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

Dixon M. R., Evans M. J., Kurdachenko L. A.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Soules P.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Otal J., Subbotin I. Ya.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Otal J.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Petrenko B. V., Subbotin I. Ya.

↓ Abstract   |   Full text (.pdf)

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

Kurdachenko L. A., Zaitsev D. I.

Full text (.pdf)

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

Article (Ukrainian)

Groups with a dense system of infinite almost normal subgroups

Kurdachenko L. A., Kuzennyi N. F., Semko N. N.

Full text (.pdf)

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

Article (Ukrainian)

Groups with minimax factor groups

Kurdachenko L. A., Pylayev V. V.

Full text (.pdf)

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

Article (Ukrainian)

Locally nilpotent groups with the min ? ∞ ? n

Kurdachenko L. A.

Full text (.pdf)

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

Article (Ukrainian)

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

Goretskii V. E., Kurdachenko L. A.

Full text (.pdf)

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

Article (Ukrainian)

Groups rich with almost-normal subgroups

Kurdachenko L. A., Pylayev V. V.

Full text (.pdf)

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

Article (Ukrainian)

Two-step nilpotent FC-groups

Kurdachenko L. A.

Full text (.pdf)

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

Article (Ukrainian)

Some classes of groups with weak minimal condition for normal subgroups

Kurdachenko L. A., Tushev A. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Kurdachenko L. A., Tushev A. V.

Full text (.pdf)

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

Article (Ukrainian)

Groups with noncyclic subgroups of finite index

Kurdachenko L. A., Pylayev V. V.

Full text (.pdf)

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

Article (Ukrainian)

FC-groups with bounded periodic part

Kurdachenko L. A.

Full text (.pdf)

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

Article (Ukrainian)

Groups with a complete system of almost-normal subgroups

Goretskii V. E., Kurdachenko L. A.

Full text (.pdf)

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

Article (Ukrainian)

Infinite groups with a generalized dense system of subnormal subgroups

Kurdachenko L. A., Kuzennyi N. F., Pylayev V. V.

Full text (.pdf)

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

Article (Ukrainian)

Nonperiodic groups with bounds for layers of elements

Kurdachenko L. A.

Full text (.pdf)

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