Groups with few maximal sum-free sets

Abstract

We show that, in contrast to the integers setting, almost all even order abelian groups $G$ have exponentially fewer maximal sum-free sets than $2^{\hat{I}¼(G)/2}$, where $\hat{I}¼(G)$ denotes the size of a largest sum-free set in $G$. This confirms a conjecture of Balogh, Liu, Sharifzadeh and Treglown.

14 pages