On the invariant E(G) for groups of odd order

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$thesmallestinteger$t$suchthateverysequenceof$t$elementsin$G$containsaproduct-onesubsequenceoflength$|G|$. In 1961, Erd\H{o}s, Ginzburg and Ziv proved that $\mathsf{E}(G)\le 2\mathrm{\mid }G\mathrm{\mid }-1$ for every finite solvable group $G$ and this result is well known as the Erd\H{o}s-Ginzburg-Ziv Theorem. In 2010, Gao and Li improved this result to $\mathsf E(G)\leq\frac{7|G|}{4}-1$andtheyconjecturedthat$\mathsf E(G)\leq \frac{3|G|}{2}$ holds for any finite non-cyclic group. In this paper, we confirm the conjecture for all finite non-cyclic groups of odd order.