Gao's conjecture on the Erdős–Ginzburg–Ziv constant

Let $G$ be a finite abelian group. Write $\eta(G)$ for the least length forcing a zero-sum subsequence of length at most $\exp(G)$, and $\mathsf{s}(G)$ for the least length forcing a zero-sum subsequence of length exactly $\exp(G)$. Here $\exp(G)$ denotes the exponent of $G$.

Gao's conjecture. For every finite abelian group $G$, one has

$$\mathsf{s}(G)=\eta(G)+\exp(G)-1.$$

This conjecture asserts equality in the general lower bound for the Erdős–Ginzburg–Ziv constant. It is a central question relating the two zero-sum invariants, and the source presents it as unresolved in general.