On D-maximal groups - Chin, Angelina Yan Mui (Università e Politecnico di Torino, 2009)
Let G be a finite p-group and let d(G) denote the cardinality of a minimal generating set of G. G is said to be d-maximal if d(H) < d(G) for any proper subgroup H of G. In this paper we show that if G is a d-maximal p-group where p is odd, then G has exponent p or p 2. For p = 2, we show that under certain conditions, a d-maximal 2-group has exponent four. We then give some classes of d-maximal p-groups. We also investigate relations between powerful p-groups and d-maximal groups.