On infinite groups whose noncyclic norm has a finite index - Liman, F. N. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
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.