Several Sufficient Conditions of a Finite p-group be an Abelian Group

An abelian Group is a direct product of several limited p-group.The abelian property of finite p-group plays an important role in studying finite group.According to analyzing subgroup of finite p-group,several conditions of abelian finite p-group have been gotten,especially,a theorem that a finite p-group is a cyclic group is gotten: |G|=pn,N is the unique p-order subgroup of G,G / N is an abelian group,if p 2,G is a cyclic group.