{"paper":{"title":"Extremal product-one free sequences in $C_q \\rtimes_s C_m$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabio Enrique Brochero Mart\\'inez, S\\'avio Ribas","submitted_at":"2016-10-31T11:20:16Z","abstract_excerpt":"Let $G$ be a finite group, written multiplicatively. The Davenport constant of $G$ is the smallest positive integer $d$ such that every sequence of $G$ with $d$ elements has a non-empty subsequence with product $1$. Let $C_n \\simeq \\mathbb Z_n$ be the cyclic group of order $n$. Bass (2007) showed that the Davenport constant of the metacyclic group $C_q \\rtimes_s C_m$, where $q$ is a prime number and $\\text{ord}_q(s) = m \\ge 2$, is $m+q-1$. In this paper, we explicit the form of all sequences $S$ of $C_q \\rtimes_s C_m$, with $q+m-2$ elements, that are free of product-$1$ subsequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09870","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"}