# Lukashova T. D.

### On the norm of decomposable subgroups in nonperiodic groups

Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1679-1689

We study the relations between the properties of nonperiodic groups and the norms of their decomposable subgroups. In particular, we analyze the influence of restrictions imposed on the norm of decomposable subgroups on the properties of the group provided that this norm is non-Dedekind. We also describe the structure of nonperiodic locally nilpotent groups for which the indicated norm is non-Dedekind . Furthermore, some relations between the norm of noncyclic Abelian subgroups and the norm of decomposable subgroups are established.

### On the Norm of Decomposable Subgroups in Locally Finite Groups

Ukr. Mat. Zh. - 2015. - 67, № 4. - pp. 480-488

We study the relationships between the norm of decomposable subgroups and the norm of Abelian noncyclic subgroups in the class of locally finite groups. We also describe some properties of periodic locally nilpotent groups in which the norm of decomposable subgroups is a non-Dedekind norm.

### On Noncyclic Norm of Infinite Locally Finite Groups

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 342-349

We study relationships between the properties of a group and its noncyclic norm. We obtain a description of infinite locally finite groups whose noncyclic norms are non-Dedekind.

### On Infinite Groups with Given Properties of the Norm of Infinite Subgroups

Ukr. Mat. Zh. - 2001. - 53, № 5. - pp. 625-630

We investigate the relationship between the norm *N* _{G}(∞) of infinite subgroups of an infinite group *G* and the structure of this group. We prove that *N* _{G}(∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if *N* _{G}(∞) is a non-Dedekind group. In both cases, we describe the structure of the group *G* under the condition that the subgroup *N* _{G}(∞) has finite index in *G*.