Minimum product sets sizes in nonabelian groups

Given a group G and integers r and s, let μG(r,s) be the minimum cardinality of the product set AB, where A and B are subsets of G of cardinality r and s, respectively. We compute μG for all nonabelian groups of order pq, where p and q are distinct odd primes, thus proving a conjecture of Deckelbaum. In addition, we apply a theorem of Eliahou and Kervaire to compute μG for all finite nilpotent groups.