The minimality conjecture for zero-sum sequences over elementary abelian 3-groups

Let $G$ be a finite abelian group, let $\mathcal A(G)$ denote the set of minimal zero-sum sequences over $G$, and let ${\rm D}(G)$ denote the Davenport constant. A set $\Omega\subset\mathcal B(G)$ is minimal with respect to $t$ when ${\mathsf d}_{\Omega}(G)=t$ and ${\mathsf d}_{\Omega'}(G)\neq t$ for every proper subset $\Omega'\subsetneq\Omega$. Elementary abelian 3-group minimality conjecture. If $G\cong\mathbb Z_3^r$ for some $r\geq 1$, then $\mathcal A(G)$ is a minimal set with respect to ${\rm D}(G)$. This conjecture concerns the remaining exponent-three case after the paper proves non-minimality in the other cases under consideration; its general status is not resolved in the supplied text.