Giovanni Vincenzi - University of Salerno

A subgroup X of‎ ‎a group G is said to be an H-‎subgroup if‎ ‎NG(X) ∩ Xg  ≤ 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, ‎ ۳ (۲۰۰۰) ۱۴۷--۱۵۶.] 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.

‎H-subgroups, T‎-groups, ‎ ‎pronormal subgroups‎, ‎weakly normal subgroups‎, ‎pronorm and H-‎norm of a group