Inverse zero-sum problems for certain groups of rank three

TL;DR

This paper solves inverse zero-sum problems related to the Erdős-Ginzburg-Ziv and η-constants for specific rank three finite abelian groups, expanding understanding of zero-sum phenomena in these algebraic structures.

Contribution

It provides the first solutions to inverse zero-sum problems for groups of the form C_2 ⊕ C_2 ⊕ C_{2n}, where n ≥ 2, for the Erdős-Ginzburg-Ziv and η-constants.

Findings

Solved inverse zero-sum problems for C_2 ⊕ C_2 ⊕ C_{2n} groups

Extended zero-sum theory to new class of rank three groups

Enhanced understanding of Erdős-Ginzburg-Ziv and η-constants in these groups

Abstract

The inverse problem associated to the Erd\H{o}s-Ginzburg-Ziv constant and the $\eta$-constant is solved for finite abelian groups of the form $C_2 \oplus C_2 \oplus C_{2n}$ where $n \ge 2$ is an integer.