L. A. Kurdachenko, N. N. Semko (Jr.), I. Ya. Subbotin, “Groups with many pronormal and transitively normal subgroups”, Algebra Discrete Math., 2012, Volume 14, Issue 1,Pages <nobr>84

This article is cited in 1 paper

RESEARCH ARTICLE

Groups with many pronormal and transitively normal subgroups

L. A. Kurdachenko^a, N. N. Semko (Jr.)^b, I. Ya. Subbotin^c

^a Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrovsk 50, Ukraine 49050
^b Department of Mathematics, National University of The State Tax Service of Ukraine, Irpen, Ukraine
^c Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA

Abstract: A subgroup $H$ of a group $G$ is said to be transitively normal in $G$, if $H$ is normal in every subgroup $K\geqslant H$ such that $H$ is subnormal in $K$. We described some infinite groups, whose non–finitely generated subgroups are transitively normal.

Keywords: soluble group, radical group, locally nilpotent group, transitively normal subgroup, non finitely generated subgroup.

MSC: 20E15, 20F19

Received: 29.05.2012
Accepted: 29.05.2012

Language: English