Exponent-order element in extremal zero-sum-free sequences

Determine whether every zero-sum-free sequence over a finite abelian group of length equal to the small Davenport constant \(\mathsf d(G)\) contains an element whose order equals the exponent of the group.

Background

The paper studies the invariant $\nu(G)$, which concerns the structure of subsequence sums of long zero-sum-free sequences over a finite abelian group. The authors note that structural information about extremal zero-sum-free sequences is known only in limited settings, particularly for cyclic groups and certain low-rank groups.

The unresolved question asks whether an extremal zero-sum-free sequence—one attaining length $\mathsf d(G)$—must contain an element of maximal possible order, namely the exponent of $G$. This issue is later connected in the paper to the behavior of the refined invariants $\nu_p(G)$.