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Inductive Methods and Zero-Sum Free Sequences

Gautami Bhowmik
  • Laboratoire Paul Painlevé, U.M.R. CNRS 8524, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France. E-mail:
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/ Immanuel Halupczok / Jan-Christoph Schlage-Puchta
  • Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104 Freiburg, Germany. E-mail:
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Published Online: 2009-11-25 | DOI: https://doi.org/10.1515/INTEG.2009.042


A fairly long-standing conjecture is that the Davenport constant of a group G = ℤn1 ⊕ ⋯ ⊕ ℤ nk with n 1 | ⋯ | nk is . This conjecture is false in general, but it remains to know for which groups it is true. By using inductive methods we prove that for two fixed integers k and it is possible to decide whether the conjecture is satisfied for all groups of the form with n co-prime to k.

We also prove the conjecture for groups of the form ℤ3 ⊕ ℤ3n ⊕ ℤ3n, where n is co-prime to 6, assuming a conjecture about the maximal zero-sum free sets in .

Keywords.: Zero-sum sequences; Davenport constant; inductive method; decidability

About the article

Received: 2009-04-23

Revised: 2009-05-22

Accepted: 2009-05-25

Published Online: 2009-11-25

Published in Print: 2009-11-01

Citation Information: Integers, Volume 9, Issue 5, Pages 515–536, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.042.

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