Conjecture on maximal sum-free sets in type I groups

Let $G$ be a finite abelian group of type I, and let $\mu(G)$ be the size of a largest sum-free subset of $G$, while $f_{\max}(G)$ is the number of maximal sum-free subsets of $G$. Type I maximal-sum-free-set conjecture. Except for the groups $\mathbb{Z}_2^k$, all type I groups $G$ have exponentially fewer maximal sum-free sets than $2^{\mu(G)/2}$.

The conjecture identifies $\mathbb{Z}_2^k$ as the likely extremal exception among type I groups. The paper proves the assertion for broad classes, but notes that new ideas are needed for the remaining even-order groups with many elements of order $2$; the full claim remains open.