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

Abstract

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 nite soluble groups in which normality is a transitive relation, J. Group Theory, 3 (2000) 147{156.) the authors showed that nite 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.