# Liman F. N.

### 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 infinite groups whose noncyclic norm has a finite index

Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 678–684

We study groups in which the intersection of normalizers of all noncyclic subgroups (noncyclic norm) has a finite index. We prove that if the noncyclic norm of an infinite noncyclic group is locally graded and has a finite index in the group, then this group is central-by-finite and its noncyclic norm is a Dedekind group.

### Groups all of whose infinite abelian pd-subgroups are normal

Ukr. Mat. Zh. - 1992. - 44, № 6. - pp. 796–800

The author studies groups in which any infinite Abelian pd-subgroup (p is a prime) is normal, on the assumption that the group indeed contains such subgroups (IH_{p}-groups). Necessary and sufficient conditions are established for a group to be an IH_{p}-group. Relationships are established between the class of IH_{p}-groups and the class of groups in which all infinite Abelian subgroups are normal, and the class of groups in which all pd-subgroups are normal.

### On groups all of whose noncyclic *pd*-subgroups are normal

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 974–980

### Nonperiodic groups in which all decomposable Pd-subgroups are normal

Ukr. Mat. Zh. - 1988. - 40, № 3. - pp. 330-335

### Groups in which every decomposable subgroup is invariant

Ukr. Mat. Zh. - 1970. - 22, № 6. - pp. 725—733