On Infinite Groups with Given Properties of the Norm of Infinite Subgroups - Lyman, F. N.; Lukashova, T. D. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
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.