Direct zero-sum problems for certain groups of rank three

Benjamin Girard; Wolfgang Schmid

doi:10.1016/j.jnt.2018.08.016

paper

Direct zero-sum problems for certain groups of rank three

arXiv:1806.07636 · doi:10.1016/j.jnt.2018.08.016

Abstract

We determine the exact value of the $η$ -constant and the multiwise Davenport constants for finite abelian groups of rank three having the form $G ≃ C_{2} \oplus C_{n_{2}} \oplus C_{n_{3}}$ with $2 ∣ n_{2} ∣ n_{3}$ . Moreover, we determine the Erdős-Ginzburg-Ziv constant of these groups under the assumption that $n_{2} /2$ has Property D or $n_{2} = n_{3}$ .

17 pages