Abstract

Given a group G and integers r and s , let μ G ( 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 μ G 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 μ G for all finite nilpotent groups.

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