On the invariant E(G) for groups of odd order

Let G be a multiplicatively written finite group. We denote by E(G) the smallest integer t such that every sequence of t elements in G contains a product-one subsequence of length |G|. In 1961, Erdős, Ginzburg and Ziv proved that E(G) ≤ 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 E(G) ≤ 7|G| 4 − 1 for every finite non-cyclic solvable group and they conjectured that E(G) ≤ 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.

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