Sum-free sets in abelian groups

Details Sum-free sets in abelian groups Sum-free sets in abelian groups

2003-07-10

arxiv.org/abs/math/0307142v4

Mathematics

Combinatorics

25 pages, even more revisions and corrections

Scientific paper

Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z in A satisfying x + y = z. We determine, for any G, the cardinality of the largest sum-free subset of G. This equals c(G)|G| where c(G) is a constant depending on G and lying in the interval [2/7,1/2]. We also estimate the number of sum-free subsets of G. It turns out that log_2 of this number is c(G)|G| + o(|G|), which is tight up to the o-term. For certain abelian groups, those whose order is divisible by a small prime of the form 3k + 2, we can obtain an asymptotic for the number of sum-free sets.

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