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

Benjamin Girard¹

¹ Centre de Mathématiques Laurent Schwartz UMR 7640 du CNRS École polytechnique 91128 Palaiseau Cedex, France

Colloquium Mathematicum, Tome 120 (2010) no. 1, pp. 7-21

Résumé

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.

Détail

DOI : 10.4064/cm120-1-2

Keywords: study minimal number elements maximal order occurring zero sumfree sequence finite abelian p group purpose general context finite abelian groups introduce number which lower upper bounds proved finite abelian p groups among other consequences method implies denote exp exponent finite abelian p group considered every zero sumfree sequence maximal possible length contains least exp elements order exp which improves previous result nbsp gao nbsp geroldinger