Sum-free sets in abelian groups

dc.creatorGreen, Ben
dc.creatorRuzsa, Imre Z.
dc.date2003-07-10
dc.date2004-11-18
dc.date.accessioned2026-07-07T04:59:34Z
dc.date.available2026-07-07T04:59:34Z
dc.descriptionLet 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.
dc.description25 pages, even more revisions and corrections
dc.identifierhttps://arxiv.org/abs/math/0307142
dc.identifierhttp://arxiv.org/abs/math/0307142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68040
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject11B75; 20D60; 20K01
dc.titleSum-free sets in abelian groups
dc.typetext

Files

Collections