RESEARCH ARTICLE

Groups with many pronormal and transitively normal subgroups

N. N. Semko (Jr.)

Department of Mathematics, National University of The State Tax Service of Ukraine, Irpen, Ukraine

Abstract: A subgroup $H$ of a group $G$ is said to be transitively normal in $G$, if $H$ is normal in every subgroup $K\geq H$ such that $H$ is subnormal in $K$. The study of radical groups, whose not finitely generated subgroups are transitively normal, has been started by L. A. Kurdachenko, N. N. Semko (Jr.), I. Ya. Subbotin. In this paper the study of such groups is continued.

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

MSC: 20E15, 2019

Received: 11.02.2013
Revised: 11.02.2013

Language: English

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