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In fact, we construct a chain of subgroups $F_n=H_0>H_1>H_2>\\cdots$, all isomorphic to $F_n$ and with trivial intersection, such that for every $i$ the only subgroups of $F_n$ containing $H_i$ are $H_i,H_{i-1},\\ldots,H_0=F_n$; in particular, each $H_{i+1}$ is maximal in $H_i$.\n  We prove that for all $n\\ge m\\ge 2$, every closed maximal subgroup of $F_m$ isomorphic to $F_n$ arises from a homeomorphism between the $n$-ary and $m$-ary Cantor spaces given by a finite sem"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.04038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-04T21:53:37Z","cross_cats_sorted":[],"title_canon_sha256":"0162c5474d87b08f0e963d04b58faee001e8e9406a79bec17ff856e0cc364a5a","abstract_canon_sha256":"ed4f8a76128cd808a9e6d294e035c7e6abf54d4d7b873d5a44e872c00e86b76b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:54.521870Z","signature_b64":"WOzQ8Mi7Jnecolc3MFrgBfEXFNMYV2EeSorqbRDovSUvH9uWsY2w9eqr7wV6Npl6wqRac3sK7Lmqs/8D2OIrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1089d7f28aa91ca9fe54f3a42f9bc09af323542e5ab62ac84c29472e9a5a5661","last_reissued_at":"2026-07-07T02:18:54.521016Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:54.521016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higman--Thompson groups $F_n$ all the way down","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gili Golan","submitted_at":"2026-07-04T21:53:37Z","abstract_excerpt":"We prove that for every $n\\ge 2$ the Higman--Thompson group $F_n$ has a maximal subgroup of infinite index isomorphic to itself. 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