{"paper":{"title":"Embedability between right-angled Artin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Sang-hyun Kim, Thomas Koberda","submitted_at":"2011-05-25T15:05:22Z","abstract_excerpt":"In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\\gam$, we produce a new graph through a purely combinatorial procedure, and call it the extension graph $\\gam^e$ of $\\gam$. We produce a second graph $\\gam^e_k$, the clique graph of $\\gam^e$, by adding extra vertices for each complete subgraph of $\\gam^e$. We prove that each finite induced subgraph $\\Lambda$ of $\\gam^e$ gives rise to an inclusion $A(\\Lambda)\\to A(\\gam)$. Conversely, we show that if there is an inclusion $A(\\Lambda)\\to A(\\gam)$ then $\\Lambda$ is an induced subgr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5056","kind":"arxiv","version":3},"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"}