An upper bound for Davenport constant of finite groups

Weidong Gao; Yuanlin Li; Jiangtao Peng

An upper bound for Davenport constant of finite groups

Number Theory 2013-08-13 v1

Authors: Weidong Gao , Yuanlin Li , Jiangtao Peng

Abstract

Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$ . We prove that $d(G)\leq \frac{|G|}{p}+9p^2-10p$ , where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal integer $\ell$ such that there is a sequence over $G$ of length $\ell$ contains no nonempty one-product subsequence.

Keywords

davenport constant finite groups product-one subsequences zero-sum problems group theory upper bound

Cite

@article{arxiv.1308.2364,
  title  = {An upper bound for Davenport constant of finite groups},
  author = {Weidong Gao and Yuanlin Li and Jiangtao Peng},
  journal= {arXiv preprint arXiv:1308.2364},
  year   = {2013}
}

Comments

arXiv admin note: text overlap with arXiv:1211.2614 by other authors

An upper bound for Davenport constant of finite groups

Abstract

Keywords

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