# Semko N. N.

### On some generalizations of nearly normal subgroups

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.

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

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.

### On Schur classes for modules over group rings

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.

### 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.

### Groups with Almost Normal Subgroups of Infinite Rank

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

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

### Structure of locally graded CDN[)-groups

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 subgroups*A* and*B* such that*A* is a proper nonmaximum subgroup, of*B*, there exists a normal subgroup*N* which belongs to*G* and satisfies the inequalities*A≤N . Fifteen types of nilpotent non-Dedekind groups and nine types of nonnilpotent locally graded groups of this kind are obtained.*

*Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Brief Communications (Ukrainian)
*

### Structure of locally graded CDN (]-groups

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.

### On the structure of CDN[]-groups

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

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

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

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

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

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

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)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
Article (Ukrainian)
*

### Structure of locally graded nonnilpotent CDN[]-groups

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

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

### Structure of separative dedekind groups

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.

### On groups close to metacyclic groups

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.

### 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

### Meta-Hamiltonian groups with elementary commutant of rank 2

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

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

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

### Groups with invariant infinite non-Abelian subgroups

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

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

### Structure of periodic metabelian metahamiltonian groups with a nonelementary commutator subgroup

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

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

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