{"paper":{"title":"Groups with Context-Free Co-Word Problem and Embeddings into Thompson's Group $V$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dana Fry, Hannah Hoganson, Heather Mathews, Johnny Gillings, Rose Berns-Zieve","submitted_at":"2014-07-29T14:53:12Z","abstract_excerpt":"Let $G$ be a finitely generated group, and let $\\Sigma$ be a finite subset that generates $G$ as a monoid. The \\emph{word problem of $G$ with respect to $\\Sigma$} consists of all words in the free monoid $\\Sigma^{\\ast}$ that are equal to the identity in $G$. The \\emph{co-word problem of $G$ with respect to $\\Sigma$} is the complement in $\\Sigma^{\\ast}$ of the word problem. We say that a group $G$ is \\emph{co$\\mathcal{CF}$} if its co-word problem with respect to some (equivalently, any) finite generating set $\\Sigma$ is a context-free language.\n  We describe a generalized Thompson group $V_{(G,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7745","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"}