Finite p-groups all of whose d-generated subgroups are powerful

Let p be an odd prime. We study d-powerful p-groups, i.e., finite p-groups all of whose d  -generated subgroups are powerful. For p≥5p≥5, we show that any powerful p-group G   is d(G)d(G)-powerful, where d(G)d(G) denotes the minimal number of generators of G. Moreover, for a finite p-group G   we prove that if there is a positive integer 2≤m