@article {Geroldinger:2011:0236-5294:323,
author = "Geroldinger, Alfred and Grynkiewicz, David and Schmid, Wolfgang",
title = "Zero-sum problems with congruence conditions",
journal = "Acta Mathematica Hungarica",
volume = "131",
number = "4",
year = "2011",
abstract = "For a finite abelian group G and a positive integer d, let <Emphasis FontCategory="SansSerif">s</Emphasis> d(G) denote the smallest integer l∈0 such that every sequence S over G of length |S|≧l has a nonempty zero-sum subsequence T of length |T|≡0 mod d. We determine <Emphasis FontCategory="SansSerif">s</Emphasis> 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 <Emphasis FontCategory="SansSerif">D</Emphasis>(G p ) is bounded above by 2exp (G p )−1. This generalizes former results for groups of rank two.",
pages = "323-345",
url = "http://www.ingentaconnect.com/content/klu/amhu/2011/00000131/00000004/00000073",
doi = "doi:10.1007/s10474-011-0073-7",
keyword = "zero-sum sequence, Erdős-Ginzburg-Ziv constant, Davenport constant, 11B30, 11P70, 20K01"
}