# Sum-free sets in abelian groups

@article{Green2003SumfreeSI,
title={Sum-free sets in abelian groups},
author={Ben Green and Imre Z. Ruzsa},
journal={Israel Journal of Mathematics},
year={2003},
volume={147},
pages={157-188}
}
• Published 10 July 2003
• Mathematics
• Israel Journal of Mathematics
LetA be a subset of an abelian groupG with |G|=n. We say thatA is sum-free if there do not existx, y, z εA withx+y=z. We determine, for anyG, the maximal densityμ(G) of a sum-free subset ofG. This was previously known only for certainG. We prove that the number of sum-free subsets ofG is 2(μ(G)+o(1))n, which is tight up to theo-term. For certain groups, those with a small prime factor of the form 3k+2, we are able to give an asymptotic formula for the number of sum-free subsets ofG. This…

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