On the Erd{\H o}s--Ginzburg--Ziv constant of finite abelian groups of high rank
Fan, Yushuang ; Gao, Weidong ; Zhong, Qinghai
arXiv, 1010.5101 / Harvested from arXiv
Text on arXiv
Let $G$ be a finite abelian group. The Erd{\H o}s--Ginzburg--Ziv constant $\mathsf s (G)$ of $G$ is defined as the smallest integer $l \in \mathbb N$ such that every sequence \ $S$ \ over $G$ of length $|S| \ge l$ \ has a zero-sum subsequence $T$ of length $|T| = \exp (G)$. If $G$ has rank at most two, then the precise value of $\mathsf s (G)$ is known (for cyclic groups this is the Theorem of Erd{\H o}s-Ginzburg-Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form $G = C_n^r$, with $n, r \in \N$ and $n \ge 2$, and we tackle the study of $\mathsf s (G)$ with a new approach, combining the direct problem with the associated inverse problem.
Publié le : 2010-10-25
Classification:  Mathematics - Number Theory 
@article{1010.5101,
     author = {Fan, Yushuang and Gao, Weidong and Zhong, Qinghai},
     title = {On the Erd{\H o}s--Ginzburg--Ziv constant of finite abelian groups of
  high rank},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1010.5101}
}

Fan, Yushuang; Gao, Weidong; Zhong, Qinghai. On the Erd{\H o}s--Ginzburg--Ziv constant of finite abelian groups of
  high rank. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1010.5101/