Direct zero-sum problems for certain groups of rank three

Abstract

We determine the exact value of the $\eta$-constant and the multiwise Davenport constants for finite abelian groups of rank three having the form $G\simeq C_2\oplus C_{n_2}\oplus C_{n_3}$ with $2\mid n_2\mid n_3$. Moreover, we determine the Erdős-Ginzburg-Ziv constant of these groups under the assumption that $n_2/2$ has Property D or $n_2=n_3$.

arXiv comment17 pages

References in corpus (3)

• Inverse zero-sum problems for certain groups of rank three
• Long $n$-zero-free sequences in finite cyclic groups
• On the Erd{ő}s-Ginzburg-Ziv constant of groups of the form $C_2^r\oplus C_n$

Cited by in corpus (6)

• On the lower bounds of Davenport constant
• Inverse zero-sum problems for certain groups of rank three
• On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups
• On an inverse problem of Erd\H os, Kleitman, and Lemke
• On a zero-sum problem arising from factorization theory
• Harborth Constants for Certain Classes of Metacyclic Groups