Direct zero-sum problems for certain groups of rank three

Benjamin Girard (1) , Wolfgang Schmid (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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 ⊕ Cn 2 ⊕ Cn 3 with 2 | n 2 | n 3. Moreover, we determine the Erd˝ os– Ginzburg–Ziv constant of these groups under the assumption that n 2 /2 has Property D or n 2 = n 3 .

Domaines: Théorie des nombres [math.NT]; Combinatoire [math.CO]; Théorie des groupes [math.GR]

Benjamin Girard, Wolfgang Schmid. Direct zero-sum problems for certain groups of rank three. 2018. ⟨hal-01817518v1⟩