Minimum product sets sizes in nonabelian groups

作者：Berchenko Kogan Yakov^*

来源：Journal of Number Theory, 2012, 132(10): 2316-2335.

DOI：10.1016/j.jnt.2012.04.011

• Sumset
• Product set
• Cauchy-Davenport theorem
• Additive number theory
• Nonabelian group

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

• 出版日期2012-10