Abstract
Ellenberg and Gijswijt gave recently a new exponential upper bound for the size of three-term arithmetic progression free sets in (Zp)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.
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