Liu–Sharifzadeh conjecture for type I groups

Let $G$ be a finite Abelian group of type I, meaning that its order is divisible by a prime congruent to $2$ modulo $3$, and let $\mu(G)$ and $f_{\max}(G)$ denote the maximum size of a sum-free subset and the number of maximal sum-free subsets of $G$, respectively. Liu–Sharifzadeh conjecture. For every type I group $G$ other than $\mathbb{Z}_2^k$, the number of maximal sum-free sets is exponentially smaller than $2^{\mu(G)/2}$. The paper reports that this conjecture is known for type I$(5)$ groups, but its stated theorem constructs counterexamples among type I groups.