{"paper":{"title":"Embeddability and universal theory of partially commutative groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Montserrat Casals-Ruiz","submitted_at":"2015-06-10T11:37:44Z","abstract_excerpt":"The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\\Gamma$, the authors introduce an infinite, locally infinite graph $\\Gamma^e$, called the extension graph of $\\Gamma$. They show that each finite induced subgraph $\\Delta$ of $\\Gamma^e$ gives rise to an embedding between the partially commutative groups $G(\\Delta)$ and $G({\\Gamma})$. Furthermore, it is proven that in many instances the converse also holds. Our first result is the decidability of the Extension Graph Embedding Problem: there is an algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03261","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"}