Small Davenport constant for higher-rank homocyclic groups

Determine the precise value of the small Davenport constant \(\mathsf d(C_n^r)\) for homocyclic groups \(C_n^r\) with rank \(r\geq 3\) and general integer \(n\geq 2\).

Background

The paper discusses the relationship between the refined invariant $\nu_p(G)$ and the orders of elements appearing in minimal zero-sum sequences of maximal length. For homocyclic groups $C_n^r$ of rank two, the relevant structural theory is settled, whereas the higher-rank case is substantially less understood.

For rank at least three, the exact value of $\mathsf d(C_n^r)$ is not known for general $n$. The authors also state that there is no conjectural description of the structure of maximal-length minimal zero-sum sequences in this general setting, but the explicitly marked open issue included here is the determination of the Davenport constant itself.