A new exponential upper bound for the Erd\H{o}s-Ginzburg-Ziv constant

TL;DR

This paper improves exponential upper bounds for the Erdős-Ginzburg-Ziv constant of finite Abelian groups by extending previous methods and results, contingent on a conjecture about Property D.

Contribution

It introduces slightly improved bounds and extends Naslund's results to all finite Abelian groups, advancing understanding of the Erdős-Ginzburg-Ziv constant.

Findings

Slightly improved exponential upper bounds for high-rank groups

Extension of bounds to arbitrary finite Abelian groups

Results depend on a conjecture about Property D

Abstract

Naslund used Tao's slice rank bounding method to give new exponential upper bounds for the Erd\H{o}s--Ginzburg-Ziv constant of finite Abelian groups of high rank. In our short manuscript we improve slightly Naslund's upper bounds. We extend Naslund's results and prove new exponential upper bounds for the Erd\H{o}s--Ginzburg-Ziv constant of arbitrary finite Abelian groups. Our main results depend on a conjecture about Property D.