Abstract
Let G be a finite (not necessarily abelian) group and let p=p(G) be the smallest prime number dividing |G|. We prove that d(G)⩽|G|p+9p2−10p, where d(G) denotes the small Davenport constant of G which is defined as the maximal integer ℓ such that there is a sequence over G of length ℓ containing no nonempty one-product subsequence.
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