2021/07/13 by Weidong Gao, Gao, Weidong, Yuanlin Li +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2107.06198
openalex publication_date 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-one subsequence of length |G|. In 1961, Erdős, Ginzburg and Ziv proved that \mathsf E(G)≤ 2|G|-1 for every finite solvable group G and this result is well known as the Erdős-Ginzburg-Ziv Theorem. In 2010, Gao and Li improved this result to \mathsf E(G)≤(7|G|)/(4)-1 and they conjectured that \mathsf 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.