Kurdachenko L. A.
On some groups all subgroups of which are nearly pronormal
Kurdachenko L. A., Russo A., Vincenzi G.
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.
Groups with weak maximality condition for nonnilpotent subgroups
Kurdachenko L. A., Semko N. N.
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.
Linear groups with minimality condition for some infinite-dimensional subgroups
Dixon M. R., Evans M. J., Kurdachenko L. A.
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.
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.
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.
Groups with Bounded Chernikov Conjugate Classes of Elements
Kurdachenko L. A., Otal J., Subbotin I. Ya.
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 x ∈ G 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).
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.
On complementability of certain generalized hypercenters in Artinian modules
Kurdachenko L. A., Petrenko B. V., Subbotin I. Ya.
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.
Groups with maximum condition for nonabelian subgroups
Kurdachenko L. A., Zaitsev D. I.
Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 925–930
Groups with a dense system of infinite almost normal subgroups
Kurdachenko L. A., Kuzennyi N. F., Semko N. N.
Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 969–973
Groups with minimax factor groups
Kurdachenko L. A., Pylayev V. V.
Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 620–625
Locally nilpotent groups with the min ? ∞ ? n
Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 340-346
Groups with weak minimality and maximality conditions for subgroups which are not normal
Goretskii V. E., Kurdachenko L. A.
Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1705–1709
Groups rich with almost-normal subgroups
Kurdachenko L. A., Pylayev V. V.
Ukr. Mat. Zh. - 1988. - 40, № 3. - pp. 326-330
Two-step nilpotent FC-groups
Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 329–335
Some classes of groups with weak minimal condition for normal subgroups
Kurdachenko L. A., Tushev A. V.
Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 457–462
Two-step solvable groups with weak minimal condition for normal subgroups
Kurdachenko L. A., Tushev A. V.
Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 300–306
Groups with noncyclic subgroups of finite index
Kurdachenko L. A., Pylayev V. V.
Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 435—440
FC-groups with bounded periodic part
Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 374 — 378
Groups with a complete system of almost-normal subgroups
Goretskii V. E., Kurdachenko L. A.
Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 42—46
Infinite groups with a generalized dense system of subnormal subgroups
Kurdachenko L. A., Kuzennyi N. F., Pylayev V. V.
Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 407–410
Nonperiodic groups with bounds for layers of elements
Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 386–389