{"paper":{"title":"Asphericity of a length four relative group presentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Abd Ghafur Bin Ahmad, Martin Edjvet, Muna A Al-Mulla","submitted_at":"2016-04-01T08:20:35Z","abstract_excerpt":"We consider the relative group presentation $\\mathcal{P} = \\langle G, \\mathbf{x} | \\mathbf{r} \\rangle$ where $\\mathbf{x} = \\{ x \\}$ and $\\mathbf{r} = \\{ xg_1 xg_2 xg_3 x^{-1} g_4 \\}$. We show modulo a small number of exceptional cases exactly when $\\mathcal{P}$ is aspherical. If $H = \\langle g_1^{-1} g_2, g_1^{-1} g_3 g_1 , g_4 \\rangle \\leq G$ then the exceptional cases occur when $H$ is isomorphic to one of $C_5,C_6,C_8$ or $C_2 \\times C_4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00163","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"}