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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: thelargest such set is contained in some maximum-size sum-free subset of thegroup. This theorem extends recent work of Balogh, Morris and Samotij, whoresolved the case G = Z_{2n}, and who obtained a weaker threshold (up to aconstant factor) in general.

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