Sum-free sets in abelian groups

By Ben Joseph Green, Imre Z. Ruzsa. 2003

153 citations recorded by the source corpus.

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 extends a result of Lev, Luczak and Schoen who found such a formula in the casen even.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5b65707d24d9854ee1248ca93c4acce9aed0fb32

Citations in the corpus

• Open problems in additive combinatorics (2007, unknown): “We mention that for all finite abelian groups G , the largest size of a sum-free subset of G is known; see [49].”