Groups with many pronormal and transitively normal subgroups

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.