On Infinite Groups with Given Properties of the Norm of Infinite Subgroups

  • F. N. Lyman
  • T. D. Lukashova


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.
How to Cite
Lyman, F. N., and T. D. Lukashova. “On Infinite Groups With Given Properties of the Norm of Infinite Subgroups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 5, May 2001, pp. 625-30, https://umj.imath.kiev.ua/index.php/umj/article/view/4285.
Research articles