{"paper":{"title":"Relatively irreducible free subroups in Out($\\mathbb{F}$)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pritam Ghosh","submitted_at":"2018-02-15T18:58:12Z","abstract_excerpt":"We prove that given a finite rank free group $\\mathbb{F}$ of rank $\\geq 3$ and two exponentially growing outer automorphisms $\\psi$ and $\\phi$ with dual lamination pairs $\\Lambda^\\pm_\\psi$ and $\\Lambda^\\pm_\\phi$ associated to them, and given a free factor system $\\mathcal{F}$ with co-edge number $\\geq 2$, $\\phi, \\psi $ each preserving $\\mathcal{F}$, so that the pair $(\\phi, \\Lambda^\\pm_\\phi), (\\psi, \\Lambda^\\pm_\\psi)$ is independent relative to $\\mathcal{F}$, then there $\\exists$ $M\\geq 1$, such that for any integer $m,n \\geq M$, the group $\\langle \\phi^m, \\psi^n \\rangle$ is a free group of ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05705","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"}