{"paper":{"title":"Erd\\H{o}s-Ginzburg-Ziv theorem and Noether number for $C_m\\ltimes_{\\varphi} C_{mn}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT","math.RA"],"primary_cat":"math.CO","authors_text":"Dongchun Han, Hanbin Zhang","submitted_at":"2017-07-12T10:43:40Z","abstract_excerpt":"Let $G$ be a multiplicative finite group and $S=a_1\\cdot\\ldots\\cdot a_k$ a sequence over $G$. We call $S$ a product-one sequence if $1=\\prod_{i=1}^ka_{\\tau(i)}$ holds for some permutation $\\tau$ of $\\{1,\\ldots,k\\}$. The small Davenport constant $\\mathsf d(G)$ is the maximal length of a product-one free sequence over $G$. For a subset $L\\subset \\mathbb N$, let $\\mathsf s_L(G)$ denote the smallest $l\\in\\mathbb N_0\\cup\\{\\infty\\}$ such that every sequence $S$ over $G$ of length $|S|\\ge l$ has a product-one subsequence $T$ of length $|T|\\in L$. Denote $\\mathsf e(G)=\\max\\{\\text{ord}(g): g\\in G\\}$. S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03639","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"}