On finite core-p2 p-groups

A p-group G is called a core-p(2) group if vertical bar H : H-G vertical bar <= p(2) 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-p(2) p-group is at most 5 if p >= 3, which is the best upper bound, and the derived length of a finite core-p(2) p-group is at most 3 if p >= 3, which is also the best upper bound. (C) 2017 Elsevier B.V. All rights reserved.