Note on the Davenport constant for finite abelian groups with rank three

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Maciej Szymon Zakarczemny

Abstract

Let G be a finite abelian group and D(G) denote the Davenport constant of G. We derive new upper bound for the Davenport constant for all finite abelian groups of rank three. Our main result is that: D(Cn1 ⊕ Cn2 ⊕ Cn3 ) ≤ (n1 − 1) + (n2 − 1) + (n3 − 1) + 1 + (a3 − 3)(n1 − 1), where 1 < n1|n2|n3 ∈ N and a3 ≤ 20369 is a constant. Therefore D(Cn1 ⊕ Cn2 ⊕ Cn3 ) grows linearly with the variables n1, n2, n3. The new result is the given upper bound for a3. Finally, we give an application of the Davenport constant to smooth numbers.

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How to Cite
Zakarczemny, M. (2021). Note on the Davenport constant for finite abelian groups with rank three. Acta Mathematica Universitatis Comenianae, 90(1), 1-6. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1409/845
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