Some finite p-groups whose normal subgroups are characteristic

Abstract

In this article, we classify some finite p-groups whose normal subgroups are characteristic. Particularly we restrict our attention to all finite p-groups of maximal class with an abelian maximal subgroup, finite 3-groups of maximal class, finite split metacyclic p-groups, minimal non-abelian p-groups and all p-groups of maximal class of order less than p 6.