{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:V7HVZ2W7KOIHUXXRMV4ISKOBZW","short_pith_number":"pith:V7HVZ2W7","schema_version":"1.0","canonical_sha256":"afcf5ceadf53907a5ef165788929c1cdb64cc0f721a81b27085fc4a348a93f02","source":{"kind":"arxiv","id":"1301.2112","version":1},"attestation_state":"computed","paper":{"title":"The number of profinite groups with a specified Sylow subgrou","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Colin D. Reid","submitted_at":"2013-01-10T13:16:34Z","abstract_excerpt":"Let $S$ be a finitely generated pro-$p$ group. Let $\\Emb(S)$ be the class of profinite groups $G$ that have $S$ as a Sylow subgroup, and such that $S$ intersects non-trivially with every non-trivial normal subgroup of $G$. In this paper, we investigate the question of whether or not $\\Emb(S)$ has finitely many isomorphism classes. For instance, we give an example where $\\Emb(S)$ contains an infinite ascending chain of soluble groups, and on the other hand show that $\\Emb(S)$ contains only finitely many isomorphism classes in the case that $S$ is just infinite."},"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":"1301.2112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-10T13:16:34Z","cross_cats_sorted":[],"title_canon_sha256":"123a18208b83cc3a74fd8e4eb7cf6db485b528a8f4d9f6c85f5fe887bd5984b4","abstract_canon_sha256":"abd6887061a52a7395b09a1f72d871ecc81959aefed407767140beffe9dd1ed0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:47.461672Z","signature_b64":"byl8oQ620O/QJ4XZ6Ad8wYi7NCYyIlV/zlz6i4ZHSycqQljuUrkwDqDGM7J211vRv58N5dfliGL/fLp7rXPGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afcf5ceadf53907a5ef165788929c1cdb64cc0f721a81b27085fc4a348a93f02","last_reissued_at":"2026-05-18T03:36:47.461198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:47.461198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of profinite groups with a specified Sylow subgrou","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Colin D. Reid","submitted_at":"2013-01-10T13:16:34Z","abstract_excerpt":"Let $S$ be a finitely generated pro-$p$ group. Let $\\Emb(S)$ be the class of profinite groups $G$ that have $S$ as a Sylow subgroup, and such that $S$ intersects non-trivially with every non-trivial normal subgroup of $G$. In this paper, we investigate the question of whether or not $\\Emb(S)$ has finitely many isomorphism classes. For instance, we give an example where $\\Emb(S)$ contains an infinite ascending chain of soluble groups, and on the other hand show that $\\Emb(S)$ contains only finitely many isomorphism classes in the case that $S$ is just infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2112","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.2112","created_at":"2026-05-18T03:36:47.461269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.2112v1","created_at":"2026-05-18T03:36:47.461269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2112","created_at":"2026-05-18T03:36:47.461269+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7HVZ2W7KOIH","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7HVZ2W7KOIHUXXR","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7HVZ2W7","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW","json":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW.json","graph_json":"https://pith.science/api/pith-number/V7HVZ2W7KOIHUXXRMV4ISKOBZW/graph.json","events_json":"https://pith.science/api/pith-number/V7HVZ2W7KOIHUXXRMV4ISKOBZW/events.json","paper":"https://pith.science/paper/V7HVZ2W7"},"agent_actions":{"view_html":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW","download_json":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW.json","view_paper":"https://pith.science/paper/V7HVZ2W7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.2112&json=true","fetch_graph":"https://pith.science/api/pith-number/V7HVZ2W7KOIHUXXRMV4ISKOBZW/graph.json","fetch_events":"https://pith.science/api/pith-number/V7HVZ2W7KOIHUXXRMV4ISKOBZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW/action/storage_attestation","attest_author":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW/action/author_attestation","sign_citation":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW/action/citation_signature","submit_replication":"https://pith.science/pith/V7HVZ2W7KOIHUXXRMV4ISKOBZW/action/replication_record"}},"created_at":"2026-05-18T03:36:47.461269+00:00","updated_at":"2026-05-18T03:36:47.461269+00:00"}