On the Erdős–Ginzburg–Ziv constant of finite abelian groups of high rank

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• 作者：Yushuang Fan^a ; ^{fys850820@163.com"" rel=""nofollow} ; Weidong Gao ; ^a ; ^{wdgao1963@yahoo.com.cn"" rel=""nofollow} ; Qinghai Zhong^a ; ^{zhongqinghai@yahoo.com.cn"" rel=""nofollow}
• 关键词：Erdő ; s– ; Ginzburg– ; Ziv constant ; Zero-sum sequences ; Inverse zero-sum problems
• 刊名：Journal of Number Theory
• 出版年：2011
• 出版时间：October 2011
• 年：2011
• 卷：131
• 期：10
• 页码：1864-1874
• 全文大小：184 K

文摘

Let G be a finite abelian group. The Erdős–Ginzburg–Ziv constant of G is defined as the smallest integer such that every sequence S over G of length Sl has a zero-sum subsequence T of length T=exp(G). If G has rank at most two, then the precise value of is known (for cyclic groups this is the theorem of Erdős–Ginzburg–Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form , with and n2, and we tackle the study of with a new approach, combining the direct problem with the associated inverse problem.