Groups whose subgroups are either abelian or pronormal

Abstract

A subgroup H of a group G is said to be pronormal in G if each of its conjugates $H^g$ in G is already conjugate to it in the subgroup $⟨H,H^g⟩$. Extending the well-known class of metahamiltonian groups, we study soluble groups in which every subgroup is abelian or pronormal.