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Wiegold also ends by saying that, in the examples he had found of an IG group with a subgroup that is not IG, the subgroup was never of finite index. Another natural question is then whether there is a subgroup of finite index in $H_3$ that is not IG. In this note we prove, for each $n\\in \\{2, 3, \\ldots\\}$, that $H_n$ and all of its finite index subgroups are"},"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":"2007.01626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-07-03T11:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"ceffb29bf0197bdb474fbb967a4b83dc725ac8ec85fb1b9a23a977830a26a4ab","abstract_canon_sha256":"18e7c07d1d05a6dc9777f8d78970cb98cc8b774145d4ff05bd427aa60f427e77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:16:03.363750Z","signature_b64":"4fiqu4XpO2l8RmsJBIkomytKKL3QDMyOBruJAF2+zSlfmkNcWzcsR2qaCHOqlCahY9gzlPuQzryX87Chri4vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77c70e2f1626efdeb83d4b88d1ed8133c449daa8cbdccf088e112f2e9558e3f4","last_reissued_at":"2026-07-05T01:16:03.363328Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:16:03.363328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariable generation and the Houghton groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Charles Garnet Cox","submitted_at":"2020-07-03T11:42:18Z","abstract_excerpt":"The Houghton groups $H_1, H_2, \\ldots$ are a family of infinite groups. 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