Zero-sum problems in finite abelian groups and affine caps

Yves Edel*, Christian Elsholtz, Alfred Geroldinger, Silke Kubertin, Laurence Rackham

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    For a finite abelian group G, let s(G) denote the smallest integer l such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence of length exp(G). We derive new upper and lower bounds for s(G), and all our bounds are sharp for special types of groups. The results are not restricted to groups G of the form G = Cnr, but they respect the structure of the group. In particular, we show s(Cn4) ≥ 20n - 19 for all odd n, which is sharp if n is a power of 3. Moreover, we investigate the relationship between extremal sequences and maximal caps in finite geometry.

    Original languageEnglish
    Pages (from-to)159-186
    Number of pages28
    JournalThe Quarterly Journal of Mathematics
    Issue number2
    Publication statusPublished - Jun 2007

    ASJC Scopus subject areas

    • Mathematics(all)


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