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

• Datum: 2001
• Hauptverfasser: Lyman, F. N., Lukashova, T. D., Лиман, Ф. Н., Лукашова, Т. Д.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2001
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4285
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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....