Groups with many pronormal and transitively normal subgroups - Kurdachenko, L.A.; Semko (Jr.), N.N.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2012)
A subgroup H of a group G is said to be transitively normal in G, if H is normal in every subgroup K ≥ H such that H is subnormal in K. We described some infinite groups, whose non–finitely generated subgroups are transitively normal.