{"paper":{"title":"On the Erd{\\H o}s--Ginzburg--Ziv constant of finite abelian groups of high rank","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qinghai Zhong, Weidong Gao, Yushuang Fan","submitted_at":"2010-10-25T12:38:28Z","abstract_excerpt":"Let $G$ be a finite abelian group. The Erd{\\H o}s--Ginzburg--Ziv constant $\\mathsf s (G)$ of $G$ is defined as the smallest integer $l \\in \\mathbb N$ such that every sequence \\ $S$ \\ over $G$ of length $|S| \\ge l$ \\ has a zero-sum subsequence $T$ of length $|T| = \\exp (G)$. If $G$ has rank at most two, then the precise value of $\\mathsf s (G)$ is known (for cyclic groups this is the Theorem of Erd{\\H o}s-Ginzburg-Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form $G = C_n^r$, with $n, r \\in \\N$ and $n \\ge 2$, and we tackle the study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5101","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}