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 122log2d+b 124)(b+1)/2,p^b(3b+4d 121)/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

Elements of minimal breadth in finite p-groups and Lie algebras

Let G be a finite p-group, and let M(G) be the subgroup generated by the non-central conjugacy classes of G of minimal size. We prove that this subgroup has class at most 3. A similar result is noted for nilpotent Lie algebras

How Groups Grow

The first book to develop from the basics, with full proofs, the cutting-edge of Group Theory: the growth of groups