{"paper":{"title":"Cohomological finiteness conditions and centralisers in generalisations of Thompson's group V","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brita E.A. Nucinkis, Conchita Martinez-Perez, Francesco Matucci","submitted_at":"2013-09-30T14:31:19Z","abstract_excerpt":"We consider generalisations of Thompson's group $V$, denoted $V_r(\\Sigma)$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, $V_r(\\Sigma)$ is the full automorphism group of a Cantor-algebra. Under some further minor restrictions, we prove that these groups are of type $\\mathrm{F}_\\infty$ and that this implies that also centralisers of finite subgroups are of type $\\mathrm{F}_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7858","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"}