{"paper":{"title":"On transitivity and (non)amenability of Aut(F_n) actions on group presentations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aglaia Myropolska, Tatiana Nagnibeda","submitted_at":"2013-09-01T22:10:31Z","abstract_excerpt":"For a finitely generated group $G$ the Nielsen graph $N_n(G)$, $n\\geq \\operatorname{rank}(G)$, describes the action of the group $\\operatorname{Aut}F_n$ of automorphisms of the free group $F_n$ on generating $n$-tuples of G by elementary Nielsen moves. The question of (non)amenability of Nielsen graphs is of particular interest in relation with the open question about Property $(T)$ for $\\operatorname{Aut}F_n$, $n\\geq 4$. We prove nonamenability of Nielsen graphs $N_n(G)$ for all $n\\ge \\max\\{2,\\operatorname{rank}(G)\\}$ when $G$ is indicable, and for $n$ big enough when $G$ is elementary amenab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0271","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"}