Random sum-free subsets of Abelian groups

Abstract

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 $p_c\approx \sqrt{\log n/n}$ above which, with high probability as $|G|\to \infty$, each such subset is contained in a maximum-size sum-free subset of $G$, whenever $q$ divides $|G|$ for some (fixed) prime $q$ with $q\equiv 2(\mathrm{mod}3)$. Moreover, in the special case $G = \ZZ_{2n}$, we determine a sharp threshold for the above property. The proof uses recent 'transference' theorems of Conlon and Gowers, together with stability theorems for sum-free subsets of Abelian groups.

31 pages, minor revision

References in corpus (2)

• Mantel's Theorem for random graphs
• Stability results for random discrete structures

Cited by in corpus (2)

• Stability results for random discrete structures
• Counting sum-free sets in Abelian groups