Let G be a multiplicatively written finite group. We denote by $\mathsf{d}(G)$ the small Davenport constant of G, that is, the maximal integer ℓ such that there is a sequence of length ℓ over G which has no non-trivial product-one subsequence. In 2014, Gao, Li, and Peng conjectured that $\mathsf{d}(G)\le |G|/p+p-2$ for any finite non-cyclic group G, where p is the smallest prime divisor of $|G|$. In this paper, we confirm that this conjecture is true.

中文翻译：

---

关于有限群的小达文波特常数猜想

令G为乘法书写的有限群。我们表示$\mathsf{d}(G)$G的小达文波特常数，即最大整数ℓ使得在G上存在长度为ℓ的序列，该序列没有非平凡的乘积一子序列。2014 年，高、李、彭推测，$\mathsf{d}(G)\le |G|/p+p-2$对于任何有限非循环群G，其中p是$|G|$. 在本文中，我们证实了这个猜想是正确的。