{"paper":{"title":"Finite groups with star-free noncyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gary L. Walls, Kaishun Wang, Xuanlong Ma","submitted_at":"2016-04-24T03:20:55Z","abstract_excerpt":"For a finite noncyclic group $G$, let $\\Cyc(G)$ be a set of elements $a$ of $G$ such that $\\langle a,b\\rangle$ is cyclic for each $b$ of $G$. The noncyclic graph of $G$ is a graph with the vertex set $G\\setminus \\Cyc(G)$, having an edge between two distinct vertices $x$ and $y$ if $\\langle x, y\\rangle$ is not cyclic. In this paper, we classify all finite noncyclic groups whose noncyclic graphs are $K_{1,n}$-free, where $3\\leq n\\leq 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06978","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"}