Product-Free Subsets of Groups, Then and Now
Name
Kedlaya Product-Free Subsets....pdf
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174.69 KB
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Author(s)
Kedlaya, Kiran S.
Date Issued
January 2009
Journal
Contemporary Mathematics
Publisher
American Mathematical Society
Citation
Kedlaya, Kiran S. "Product-free subsets of groups, then and now." in Contemporary Mathematics, American Mathematical Society, v.479, p.169, 2009.
Version
Author's final manuscript
Abstract
Let G be a group. A subset S of G is product-free if there do not exist a, b, c ∈ S
(not necessarily distinct1) such that ab = c.
One can ask about the existence of large product-free subsets for various groups,
such as the groups of integers (see next section), or compact topological groups (as
suggested in [11]). For the rest of this paper, however, I will require G to be a finite
group of order n > 1. Let α(G) denote the size of the largest product-free subset
of G; put β(G) = α(G)/n, so that β(G) is the density of the largest product-free
subset. What can one say about α(G) or β(G) as a function of G, or as a function
of n? (Some of our answers will include an unspecified positive constant; I will
always call this constant c.)
Description
Dedicated to Joe Gallian on his 65th birthday and the 30th anniversary of the Duluth REU
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
http://www.jointmathematicsmeetings.org/bookstore?fn=20&arg1=conmseries&ikey=CONM-479
