{"paper":{"title":"On the smallest non-abelian quotient of $\\mathrm{Aut}(F_n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Barbara Baumeister, Dawid Kielak, Emilio Pierro","submitted_at":"2017-05-08T14:05:18Z","abstract_excerpt":"We show that the smallest non-abelian quotient of $\\mathrm{Aut}(F_n)$ is $\\mathrm{PSL}_n(\\mathbb{Z}/2\\mathbb{Z}) = \\mathrm{L}_n(2)$, thus confirming a conjecture of Mecchia--Zimmermann. In the course of the proof we give an exponential (in $n$) lower bound for the cardinality of a set on which $\\mathrm{SAut}(F_n)$, the unique index $2$ subgroup of $\\mathrm{Aut}(F_n)$, can act non-trivially. We also offer new results on the representation theory of $\\mathrm{SAut(F_n)}$ in small dimensions over small, positive characteristics, and on rigidity of maps from $\\mathrm{SAut}(F_n)$ to finite groups of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02885","kind":"arxiv","version":2},"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"}