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) ∩ 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, 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. [ABSTRACT FROM AUTHOR]