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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-2,
author = {Benjamin Girard},
title = {Inverse zero-sum problems in finite Abelian p-groups},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {7-21},
zbl = {1246.11062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-2}
}
Benjamin Girard. Inverse zero-sum problems in finite Abelian p-groups. Colloquium Mathematicae, Tome 120 (2010) pp. 7-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-2/