Title: The Erdős-Ginzburg-Ziv constant and progression-free subsets,
Abstract: Ellenberg and Gijswijt gave recently a new exponential upper bound for the
size of three-term arithmetic progression free sets in $({\mathbb Z_p})^n$,
where $p$ is a prime. Petrov summarized their method and generalized their
result to linear forms.
In this short note we use Petrov's result to give new exponential upper
bounds for the Erdős-Ginzburg-Ziv constant of finite Abelian groups of high
rank. Our main results depend on a conjecture about Property D.