{"paper":{"title":"On the Erd{\\H{o}}s-Ginzburg-Ziv constant of groups of the form $C_2^r\\oplus C_n$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Qinghai Zhong, Yushuang Fan","submitted_at":"2015-03-20T13:46:51Z","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 $|S|\\geq l$ has a zero-sum subsequence $T$ of length $|T|= {\\exp}(G)$. The value of this classical invariant for groups with rank at most two is known. But the precise value of $\\mathsf s(G)$ for the groups of rank larger than two is difficult to determine. In this paper we pay our attentions to the groups of the form $C_2^{r-1}\\oplus C_{2n}$, where $r\\geq 3$ and $n\\ge 2$. We give a new upper bound of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06070","kind":"arxiv","version":1},"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"}