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On Davenport’s constant of finite abelian groups. (English) Zbl 1149.11301
Authors’ abstract: “Let \(G\) be a finite abelian group, the Davenport constant \(\mathsf D(G)\) is the smallest integer \(d\) such that every sequence of \(d\) elements in \(G\) contains a nonempty zero-sum subsequence. In this paper, we confirm in part some conjectures on Davenport’s constant \(\mathsf D(G)\) by determining the exact value of \(\mathsf D(G)\) for some new \(G\).”
Here it is studied when \(G\) is of the form \(G=H\oplus C_{m,n}\), where \(m\) is a multiple of the exponent \(\exp(H)\) of \(H\) and \(n\) is a positive integer and either \(m\) or \(n\) being large with respect to various invariants of \(H\). One of their main results is the following: Theorem 3. If \(\mathsf D(H\oplus C_{m,n})=\mathsf D(H)+m-1\) and \(m\geq (| H| -1)\exp(H)-\mathsf D(H)+1\), then \(\mathsf D(G)=\mathsf D(H)+nm-1\).

MSC:
11B75 Other combinatorial number theory
20K01 Finite abelian groups
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