{"paper":{"title":"Automorphism towers of groups of homeomorphisms of Cantor space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Feyishayo Olukoya","submitted_at":"2019-08-10T21:53:08Z","abstract_excerpt":"We show that for any full and sufficiently transitive (i.e. \\textit{flexible}) group $G$ of homeomorphisms of Cantor space, $\\mathrm{Aut}(\\mathrm{Aut}(G)) = \\mathrm{Aut}(G)$. This class contains many generalisations of the Higman-Thompson groups $G_{n,r}$, and the Rational group $\\mathcal{R}_{2}$ of Grigorchuk, Nekrashevych, and Suchanski{\\u \\i}. We also demonstrate that for generalisations $T_{n,r}$ of R. Thompson's group $T$, $\\mathrm{Aut}(\\mathrm{Aut}(T_{n,r}))= \\mathrm{Aut}(T_{n,r})$. In the case of the groups $G_{n,r}$ and $T_{n,r}$ our results extend results of Brin and Guzm{\\' a}n for T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03815","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03815/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}