A Classification of Finite Metahamiltonian p-Groups

A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G . If G is non-nilpotent, then the structure of G has been determined. If G is nilpotent, then the structure of G is determined by the structure of its Sylow subgroups. However, the classification of finite metahamiltonian p -groups is an unsolved problem. In this paper, finite metahamiltonian p -groups are completely classified up to isomorphism.