{"paper":{"title":"Simple groups separated by finiteness properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky, Rachel Skipper, Stefan Witzel","submitted_at":"2017-12-14T17:41:39Z","abstract_excerpt":"We show that for every positive integer $n$ there exists a simple group that is of type $\\mathrm{F}_{n-1}$ but not of type $\\mathrm{F}_n$. For $n\\ge 3$ these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace--R\\'emy, consists of non-affine Kac--Moody groups over finite fields. Our examples arise from R\\\"over--Nekrashevych groups, and contain free abelian groups of infinite rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05361","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"}