Sum-free sets in abelian groups

Ben Green, Imre Z. Ruzsa

Research output: Contribution to journalArticle

53 Citations (Scopus)


Let A be a subset of an abelian group G with |G| = n. We say that A is sum-free if there do not exist x, y, z ∈ A with x + y = z. We determine, for any G, the maximal density μ(G) of a sum-free subset of G. This was previously known only for certain G. We prove that the number of sum-free subsets of G is 2(μ(G)+o(1))n, which is tight up to the o-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 of G. This extends a result of Lev, Łuczak and Schoen who found such a formula in the case n even.

Original languageEnglish
Pages (from-to)157-188
Number of pages32
JournalIsrael Journal of Mathematics
Publication statusPublished - Jan 1 2005

ASJC Scopus subject areas

  • Mathematics(all)

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