On the invariant $\mathsf E(G)$ for groups of odd order
Volume 201 / 2021
Acta Arithmetica 201 (2021), 255-267
MSC: Primary 11B75; Secondary 11P70.
DOI: 10.4064/aa210317-1-6
Published online: 9 November 2021
Abstract
Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-1 subsequence of length $|G|$. In 1961, Erdős, Ginzburg and Ziv proved that $\mathsf E(G)\leq 2|G|-1$ for every finite cyclic group $G$, and this result is well known as the Erdős–Ginzburg–Ziv Theorem. In 2010, Gao and Li proved that $\mathsf E(G)\leq 7|G|/4-1$ for every finite non-cyclic solvable group and they conjectured that $\mathsf E(G)\leq 3|G|/2$ holds for any finite non-cyclic group. In this paper, we confirm the conjecture for all finite non-cyclic groups of odd order.
