A characterization of soluble groups in which normality is a transitive relation

A subgroup $X$ of‎ ‎a group $G$ is said to be an H-‎subgroup if‎ ‎NG(X) ∩ X^g ≤ X for each element $g$ belonging to $G$‎. ‎In [M‎. ‎Bianchi and e.a.‎, ‎On finite soluble groups in which normality is a transitive relation‎, J‎. ‎Group Theory, ‎3 (2000) 147-156.] the authors showed that finite groups in which every subgroup has the H‎‎-property are exactly soluble groups in which normality is a transitive relation‎. ‎Here we extend this characterization to groups without simple sections‎.