The sharp threshold for maximum-size sum-free subsets in even-order abelian groups

We study sum-free sets in sparse random subsets of even order abelian groups. In particular, we determine the sharp threshold for the following property: the largest such set is contained in some maximum-size sum-free subset of the group. This theorem extends recent work of Balogh, Morris and Samoti...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Bushaw, Neal, Maurício Collares Neto, Morris, Robert, Smith, Paul
Format: Article
Language:English
Subjects:
Group theory
Online Access:Get full text
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Summary:We study sum-free sets in sparse random subsets of even order abelian groups. In particular, we determine the sharp threshold for the following property: the largest such set is contained in some maximum-size sum-free subset of the group. This theorem extends recent work of Balogh, Morris and Samotij, who resolved the case G = Z_{2n}, and who obtained a weaker threshold (up to a constant factor) in general.
ISSN:2331-8422
DOI:10.48550/arxiv.1310.3236