{"paper":{"title":"Elementary subgroups of the free group are free factors - a new proof","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.LO","authors_text":"Chlo\\'e Perin","submitted_at":"2019-03-14T09:48:24Z","abstract_excerpt":"In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group $\\mathbb{F}$ must be a free factor. The proof is based on definability of orbits of elements of under automorphisms of $\\mathbb{F}$ fixing a large enough subset of $\\mathbb{F}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05876","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"}