The breadth-degree type of a finite p-group

In the present paper we show that a stem finite p-group G has size bounded by min(p^(8d−2log2d+b−4)(b+1)/2,p^b(3b+4d−1)/2) where b is the breadth of G and pd is the maximum character degree of G. As a consequence there are only finitely many finite stem p-groups having breadth b and maximum character degree pd.