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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