Geodesic
Groups with many pronormal and transitively normal subgroups
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 269-286.

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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. 
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N. N. Semko (Jr.). Groups with many pronormal and transitively normal subgroups. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 269-286. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a9/

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