On the norm of decomposable subgroups in nonperiodic groups

Abstract

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.