Inverse zero-sum problems in finite Abelian $p$-groups

Volume 120 / 2010

Benjamin Girard Colloquium Mathematicum 120 (2010), 7-21 MSC: 11R27, 11B75, 11P70, 20D60, 20K01, 05E99, 13F05. DOI: 10.4064/cm120-1-2


We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian $p$-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian $p$-groups. Among other consequences, our method implies that, if we denote by $\exp(G)$ the exponent of the finite Abelian $p$-group $G$ considered, every zero-sumfree sequence $S$ with maximal possible length over $G$ contains at least $\exp(G)-1$ elements of order $\exp(G)$, which improves a previous result of W. Gao and A. Geroldinger.


  • Benjamin GirardCentre de Mathématiques Laurent Schwartz
    UMR 7640 du CNRS
    École polytechnique
    91128 Palaiseau Cedex, France

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