{"paper":{"title":"On rank of the join of two subgroups in a free group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Sergei V. Ivanov","submitted_at":"2016-08-01T21:02:05Z","abstract_excerpt":"Let $H, K$ be two finitely generated subgroups of a free group, let $\\langle H, K \\rangle$ denote the subgroup generated by $H, K$, called the join of $H, K$, and let neither of $H$, $K$ have finite index in $\\langle H, K \\rangle$. We prove the existence of an epimorphism $\\zeta : \\langle H, K \\rangle \\to F_2$, where $F_2$ is a free group of rank 2, such that the restriction of $\\zeta$ on both $H$ and $K$ is injective and the restriction $\\zeta_0 : H \\cap K \\to \\zeta (H) \\cap \\zeta (K) $ of $\\zeta$ on $H \\cap K $ to $\\zeta (H) \\cap \\zeta (K)$ is surjective. This is obtained as a corollary of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00617","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"}