On zero-sum subsequences of length [formula omitted

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Let G be an additive finite abelian group of exponent exp(G). For every positive integer k, let 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). We prove that if exp(G) is sufficiently larger than |G|exp(G) then skexp(G)(G)=kexp(G)+D(G)−1 for all k⩾2, where D(G) is the Davenport constant of G.