Conjecture on the extremal number of maximal sum-free sets in abelian groups

Let $G$ be an abelian group of order $n$, and let $f_{\max}(G)$ denote the number of maximal sum-free subsets of $G$.

Extremal bounds conjecture.

$$2^{n/7} \leq f_{\max}(G) \leq 2^{n/4+o(n)},$$

where both bounds are best possible.

This conjecture predicts the correct range, up to the stated asymptotic term, for the number of maximal sum-free sets in an abelian group. It was motivated by the bounds $2n/7\leq\mu(G)\leq n/2$ for the relevant group parameter; the supplied text gives no resolution status.