{"paper":{"title":"On the generation problem in Thompson's groups $F_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eytan Sapir, Gili Golan","submitted_at":"2026-05-30T19:29:13Z","abstract_excerpt":"We study the generation problem in the Higman-Thompson groups $F_n$ via the core and closure of subgroups of $F_n$ and associated automata. We give sufficient conditions for a subset $X \\subseteq F_n$ to generate $F_n$, and provide an algorithm which verifies these conditions when $X$ is finite. As an application, we answer a question of Aiello and Nagnibeda, motivated by Savchuk's problem on maximal subgroups of Thompson's group $F$. Specifically, we show that for every $n\\geq 2$, the Higman-Thompson group $F_n$ contains a maximal subgroup of infinite index which fixes no point of $(0,1)$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00863","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00863/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"}