Random sum-free subsets of abelian groups

József Balogh, Robert Morris, Wojciech Samotij

Research output: Contribution to journalArticlepeer-review


We characterize the structure of maximum-size sum-free subsets of a random subset of an abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = ℤ2n, we determine the sharp threshold for the above property. The proof uses recent ‘transference’ theorems of Conlon and Gowers, together with stability theorems for sum-free sets of abelian groups.

Original languageEnglish (US)
Pages (from-to)651-685
Number of pages35
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Mar 1 2014

ASJC Scopus subject areas

  • Mathematics(all)


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