{"paper":{"title":"On the local-indicability Cohen-Lyndon Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Peter A. Linnell, Warren Dicks, Yago Antol\\'in","submitted_at":"2010-02-09T18:15:39Z","abstract_excerpt":"For a group $H$ and a subset $X$ of $H$, we let ${}^HX$ denote the set $\\{hxh^{-1} \\mid h \\in H, x \\in X\\}$, and when $X$ is a free-generating set of $H$, we say that the set ${}^HX$ is a Whitehead subset of $H$.\n  For a group $F$ and an element $r$ of $F$, we say that $r$ is Cohen-Lyndon aspherical in $F$ if ${}^F\\{r\\}$ is a Whitehead subset of the subgroup of $F$ that is generated by ${}^F\\{r\\}$.\n  In 1963, D. E. Cohen and R. C. Lyndon independently showed that in each free group each non-trivial element is Cohen-Lyndon aspherical.\n  In 1987, M. Edjvet and J. Howie showed that if $A$ and $B$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1934","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"}