Sum-free sets in abelian groups

BJ Green

Research output: Contribution to journalArticle (Academic Journal)peer-review

63 Citations (Scopus)


Let A be a subset of an abelian group G with vertical bar G vertical bar = n. We say that A is sum-free if there do not exist x, y, z is an element of A with x + y = z. We determine, for any G, the maximal density mu(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((mu(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, Luczak and Schoen who found such a formula in the case n even.
Translated title of the contributionSum-free sets in abelian groups
Original languageEnglish
Pages (from-to)157 - 188
JournalIsrael Journal of Mathematics
Publication statusPublished - 2005

Bibliographical note

Publisher: Magnes Press, Hebrew University
Other identifier: IDS Number: 959AO


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