On Two Special D₁-groups

Let G be a finite p-group. If the order of the derived subgroup of each proper subgroup of G divides pi,then G is called a Di-group. In this paper, using the classification of.Di-groups, we classify the finite p-groups satisfying the following conditions respectively:(1) every non-abelian max-imal subgroup is isomorphic the direct product of a minimal non-abelian subgroup and a cyclic group; (2) every non-abelian maximal subgroups is isomorphic the direct product of a minimal non-abelian subgroup and a abelian group. This answer two problems introduced by Berkovich and Janko.