On finite core-p2p-groups

A p-group G is called a core-p2 group if |H:HG|≤p2 for every subgroup H of G (where HG denotes the normal core of H in G). In this paper, it is proved that the nilpotent class of a finite core-p2p-group is at most 5 if p≥3, which is the best upper bound, and the derived length of a finite core-p2p-group is at most 3 if p≥3, which is also the best upper bound.