On a conjecture of the small Davenport constant for finite groups

Abstract

Let G be a multiplicatively written finite group. We denote by 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 d(G)≤|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.