2019
Том 71
№ 9

All Issues

Semko N. N.

Articles: 19
Article (Ukrainian)

On some generalizations of nearly normal subgroups

Piskun M. M., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1381-1395

A subgroup $H$ of a group $G$ is called almost polycyclically close to a normal group (in $G$) if $H$ contains a subgroup $L$ normal in $H^G$ for which the quotient group $H^G /L$ is almost polycyclic. The group G is called an anti-$PC$-group if each its subgroup, which is not almost polycyclic, is almost polycyclically close to normal. The structure of minimax anti-$PC$-groups is investigated.

Article (Russian)

On the application of some concepts of ring theory to the study of the influence of systems of subgroups of a group

Piskun M. M., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 657–668

We study the groups, in which the family Lnon-nn(G) of all not nearly normal subgroups has the Krull dimension. A subgroup H of the group G is said to be nearly normal if H has finite index in its normal closure.

Article (Russian)

On Schur classes for modules over group rings

Chupordya V. A., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1261–1268

We consider the problem of the coupling between a factor-module $A / C_A(G)$ and a submodule $A(\omega RG)$, where $G$ is a group, $R$ is a ring, and $A$ is an $RG$-module. It is possible to consider $C_A (G)$ as an analog of the center of the group and the submodule $A(\omega RG)$ as an analog of the derived subgroup of the group.

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 (Ukrainian)

Groups with Almost Normal Subgroups of Infinite Rank

Kuchmenko S. N., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 514–532

We study classes of groups whose subgroups of some infinite ranks are almost normal.

Article (Ukrainian)

Structure of locally graded CDN[)-groups

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 383–388

We introduce the notion of CDN[)-groups:G is a CDN[)-group if, for any pair of its subgroupsA andB such thatA is a proper nonmaximum subgroup, ofB, there exists a normal subgroupN which belongs toG and satisfies the inequalitiesA≤N. Fifteen types of nilpotent non-Dedekind groups and nine types of nonnilpotent locally graded groups of this kind are obtained.

Article (Ukrainian)

Structure of locally graded CDN (]-groups

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1532–1536

We introduce the notion of a CDN(]-group G, namely, a group such that, for any pair of its subgroups A and B such that A is a proper nonmaximal subgroup of B, there exists a normal subgroup N of G and A < N ≤ B. Thirteen types of non-Dedekind nilpotent groups and 9 types of nonnilpotent locally graded groups of this kind are described.

Article (Ukrainian)

On the structure of CDN[]-groups

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1250–1261

We describe nilpotent non-Dedekind CDN[]-groups.

Article (Ukrainian)

On the construction of CDN[]-groups with elementary commutant of rank two

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1396–1403

We describe certain CDN-groups of order p n with elementary commutant of rank two.

Brief Communications (Ukrainian)

Structure of one class of groups with conditions of denseness of normality for subgroups

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 8. - pp. 1148–1151

We give a constructive description of locally graded groups G satisfying the following condition: For any pair of subgroups A and B such that A, there exists a normal subgroup N that belongs to G and is such that A≦N≦B.

Article (Ukrainian)

Structure of locally graded nonnilpotent CDN[]-groups

Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 789–798

We prove a theorem that gives a constructive description of locally graded nonnilpotent CDN []-groups.

Article (Ukrainian)

Structure of separative dedekind groups

Kuzennyi N. F., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1342-1351

We describe groups such that all their subgroups that do not belong to a certain proper subgroup are normal. We also solve the separate problem of description of such groups with normal non-Abelian subgroups.

Article (Ukrainian)

On groups close to metacyclic groups

Kuzennyi N. F., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 782-790

We study groups whose structure is similar to the structure of metacyclic groups. These groups play an important role in the investigation of groups with normal subgroups.

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)

Meta-Hamiltonian groups with elementary commutant of rank 2

Kuzennyi N. F., Semko N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 168–175

Article (Ukrainian)

Structure of periodic met-abelian meta-hamiltonian groups with elementary commutant of rank 2

Kuzennyi N. F., Semko N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 743-750

Article (Ukrainian)

Groups with invariant infinite non-Abelian subgroups

Kuzennyi N. F., Levishchenko S. S., Semko N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 3. - pp. 314-321

Article (Ukrainian)

Structure of periodic metabelian metahamiltonian groups with a nonelementary commutator subgroup

Kuzennyi N. F., Semko N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 180-185

Article (Ukrainian)

Some non-Abelian groups with a prescribed system of invariant infinite Abelian subgroups

Semko N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 2. - pp. 270–273