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Acta Mathematica Hungarica
Alfred Geroldinger
David J. Grynkiewicz
, and
Wolfgang A. Schmid


For a finite abelian group G and a positive integer d, let s d(G) denote the smallest integer ∊ℕ0 such that every sequence S over G of length |S|≧ has a nonempty zero-sum subsequence T of length |T|≡0 mod d. We determine s d(G) for all d≧1 when G has rank at most two and, under mild conditions on d, also obtain precise values in the case of p-groups. In the same spirit, we obtain new upper bounds for the Erdős–Ginzburg–Ziv constant provided that, for the p-subgroups G p of G, the Davenport constant D(G p ) is bounded above by 2exp  (G p )−1. This generalizes former results for groups of rank two.

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