On zero-sum subsequences of length kexp(G)kexp(G)

Let G   be an additive finite abelian group of exponent exp(G)exp(G). For every positive integer k  , let skexp(G)(G)skexp(G)(G) denote the smallest integer t such that every sequence over G of length t   contains a zero-sum subsequence of length kexp(G)kexp(G). We prove that if exp(G)exp(G) is sufficiently larger than |G|exp(G) then skexp(G)(G)=kexp(G)+D(G)−1skexp(G)(G)=kexp(G)+D(G)−1 for all k⩾2k⩾2, where D(G)D(G) is the Davenport constant of G.