On infinite groups whose noncyclic norm has a finite index
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.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 5, pp 755-762.
Citation Example: Liman F. N. On infinite groups whose noncyclic norm has a finite index // Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 678–684.