The Erdős-Ginzburg-Ziv constant of a finite abelian group G, denoted $\mathfrak{s}(G)$, is the smallest $k\in \mathbb{N}$ such that any sequence of elements of G of length k contains a zero-sum subsequence of length $\exp (G)$. In this paper, we use the partition rank from [14], which generalizes the slice rank, to prove that for any odd prime p,$\mathfrak{s}\left({\mathbb{F}}_p^n\right)\le (p-1)2^p{(J(p)\cdot p)}^n$ where $0.8414<J(p)<0.91837$. For large n, and $p>3$, this is the first exponential improvement to the trivial bound. We also provide a near optimal result conditional on the conjecture that ${(\mathbb{Z}/k\mathbb{Z})}^n$ satisfies property D, as defined in [9], showing that in this case$\mathfrak{s}\left({(\mathbb{Z}/k\mathbb{Z})}^n\right)\le (k-1)4^n+k.$

有限阿贝尔群G的Erdős-Ginzburg-Ziv常数，表示为$\mathfrak{s}（G）$，是最小的 $ķ\in \mathbb{ñ}$使得元件的任何序列ģ长度的ķ包含长度的零和子序列$\mathrm{经验值}（G）$。在本文中，我们使用[14]中的划分等级，对划分等级进行了概括，证明对于任何奇数素数p，$\mathfrak{s}（{\mathbb{F}}_p^{ñ}）\le （p-\mathrm{1个}）2^p{（Ĵ（p）\cdot p）}^{ñ}$ 哪里 $0.8414<Ĵ（p）<0.91837$。对于大n，和$p>3$，这是对微不足道范围的首次指数改进。我们还根据以下猜想提供了接近最佳的结果：${（\mathbb{ž}/ķ\mathbb{ž}）}^{ñ}$满足[9]中定义的属性D，表明在这种情况下$\mathfrak{s}（{（\mathbb{ž}/ķ\mathbb{ž}）}^{ñ}）\le （ķ-\mathrm{1个}）4^{ñ}+ķ。$