{"paper":{"title":"Virtually abelian subgroups of $IA_n(Z/3)$ are abelian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lee Mosher, Michael Handel","submitted_at":"2018-01-28T15:25:39Z","abstract_excerpt":"When studying subgroups of $Out(F_n)$, one often replaces a given subgroup $H$ with one of its finite index subgroups $H_0$ so that virtual properties of $H$ become actual properties of $H_0$. In many cases, the finite index subgroup is $H_0 = H \\cap IA_n(Z/3)$. For which properties is this a good choice? Our main theorem states that being abelian is such a property. Namely, every virtually abelian subgroup of $IA_n(Z/3)$ is abelian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09241","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"}