{"paper":{"title":"Harborth Constants for Certain Classes of Metacyclic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Noah Kravitz","submitted_at":"2018-07-12T18:52:39Z","abstract_excerpt":"The Harborth constant of a finite group $G$ is the smallest integer $k\\geq \\exp(G)$ such that any subset of $G$ of size $k$ contains $\\exp(G)$ distinct elements whose product is $1$. Generalizing previous work on the Harborth constants of dihedral groups, we compute the Harborth constants for the metacyclic groups of the form $H_{n, m}=\\langle x, y \\mid x^n=1, y^2=x^m, yx=x^{-1}y \\rangle$. We also solve the \"inverse\" problem of characterizing all smaller subsets that do not contain $\\exp(H_{n,m})$ distinct elements whose product is $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04785","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"}