L. A. Kurdachenko, I. Ya. Subbotin, T. V. Velychko, “On the non-periodic groups, whose subgroups of infinite special rank are transitively normal”, Algebra Discrete Math., 2020, Volume 29, Issue 1,Pages <nobr>74

This article is cited in 2 papers

RESEARCH ARTICLE

On the non-periodic groups, whose subgroups of infinite special rank are transitively normal

L. A. Kurdachenko^a, I. Ya. Subbotin^b, T. V. Velychko^a

^a Department of Geometry and Algebra, Dnipro National University, 72 Gagarin Av., Dnipro, Ukraine 49010
^b Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA

Abstract: This paper devoted to the non-periodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a group $G$ includes an ascendant locally nilpotent subgroup of infinite special rank, then $G$ is abelian.

Keywords: finite special rank, soluble group, periodic group, locally nilpotent radical, locally nilpotent residual, transitively normal subgroups.

MSC: Primary 20E15, 20F16; Secondary 20E25, 20E34, 20F22, 20F50

Received: 17.03.2019

Language: English

DOI: 10.12958/adm1357