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|a Kedlaya, Kiran S.
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Kedlaya, Kiran S.
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|a Kedlaya, Kiran S.
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|a Product-Free Subsets of Groups, Then and Now
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|b American Mathematical Society,
|c 2011-06-21T15:27:21Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/64627
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|a Dedicated to Joe Gallian on his 65th birthday and the 30th anniversary of the Duluth REU
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|a 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.)
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|t Contemporary Mathematics
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