Minimum product set sizes in nonabelian groups of order pq
Name
Deckelbaum-2009-Minimum product set.pdf
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205.69 KB
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Author(s)
Deckelbaum, Alan T.
Date Issued
March 2009
Journal
Journal of Number Theory
Publisher
Elsevier
Citation
Deckelbaum, Alan. “Minimum Product Set Sizes in Nonabelian Groups of Order Pq.” Journal of Number Theory 129, no. 6 (June 2009): 1234–1245. © 2009 Elsevier Inc.
Version
Final published version
Abstract
Let G be a nonabelian group of order pq, where p and q are distinct odd primes. We analyze the minimum product set cardinality μG(r,s)=min|AB|μG(r,s)=min|AB|, where A and B range over all subsets of G of cardinalities r and s , respectively. In this paper, we completely determine μG(r,s)μG(r,s) in the case where G has order 3p and conjecture that this result can be extended to all nonabelian groups of order pq. We also prove that for every nonabelian group of order pq there exist 1⩽r,s⩽pq1⩽r,s⩽pq such that μG(r,s)>μZ/pqZ(r,s)μG(r,s)>μ[subscript Z over pqZ(r,s)].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1016/j.jnt.2009.02.006
