{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QHCQ5LKLVRLVDS5LW7R34ME6EG","short_pith_number":"pith:QHCQ5LKL","schema_version":"1.0","canonical_sha256":"81c50ead4bac5751cbabb7e3be309e218b5ec8cfbbd1857200b388ff2ae7e3e8","source":{"kind":"arxiv","id":"1002.4853","version":5},"attestation_state":"computed","paper":{"title":"On the Connectivity of the Sylow Graph of a Finite Group","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Francesco G. Russo (Universita' degli Studi di Palermo, Italy), Palermo","submitted_at":"2010-02-25T19:34:27Z","abstract_excerpt":"The Sylow graph $\\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\\mathbf{N}$--closed classes of groups. The connectivity of $\\Gamma(G)$ was proved only few years ago, involving the classification of finite simple groups, and the structure of $G$ may be strongly restricted, once information on $\\Gamma(G)$ are given. The first result of the present paper deals with a condition on $\\mathbf{N}$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $\\Gamma(G)$."},"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":"1002.4853","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2010-02-25T19:34:27Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"607457b415a1e2ba78a7b9738bab7922199c453f2911ecd4cda1ecb6526764cb","abstract_canon_sha256":"e5380c9433d6b60e7002480b28a02575029b0e70642c3d71be831ee883224834"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:03.762218Z","signature_b64":"yt2lbnlkxwbc2sofYXwgDjzsD3Kv9e2i3gdXwmwt4ncBtbu6AWICsBuD0q4+771StsOAyRkEosuOPmcswHkZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81c50ead4bac5751cbabb7e3be309e218b5ec8cfbbd1857200b388ff2ae7e3e8","last_reissued_at":"2026-05-18T03:40:03.761638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:03.761638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Connectivity of the Sylow Graph of a Finite Group","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Francesco G. Russo (Universita' degli Studi di Palermo, Italy), Palermo","submitted_at":"2010-02-25T19:34:27Z","abstract_excerpt":"The Sylow graph $\\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\\mathbf{N}$--closed classes of groups. The connectivity of $\\Gamma(G)$ was proved only few years ago, involving the classification of finite simple groups, and the structure of $G$ may be strongly restricted, once information on $\\Gamma(G)$ are given. The first result of the present paper deals with a condition on $\\mathbf{N}$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $\\Gamma(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4853","kind":"arxiv","version":5},"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":"1002.4853","created_at":"2026-05-18T03:40:03.761733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.4853v5","created_at":"2026-05-18T03:40:03.761733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4853","created_at":"2026-05-18T03:40:03.761733+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHCQ5LKLVRLV","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHCQ5LKLVRLVDS5L","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHCQ5LKL","created_at":"2026-05-18T12:26:12.377268+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/QHCQ5LKLVRLVDS5LW7R34ME6EG","json":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG.json","graph_json":"https://pith.science/api/pith-number/QHCQ5LKLVRLVDS5LW7R34ME6EG/graph.json","events_json":"https://pith.science/api/pith-number/QHCQ5LKLVRLVDS5LW7R34ME6EG/events.json","paper":"https://pith.science/paper/QHCQ5LKL"},"agent_actions":{"view_html":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG","download_json":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG.json","view_paper":"https://pith.science/paper/QHCQ5LKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.4853&json=true","fetch_graph":"https://pith.science/api/pith-number/QHCQ5LKLVRLVDS5LW7R34ME6EG/graph.json","fetch_events":"https://pith.science/api/pith-number/QHCQ5LKLVRLVDS5LW7R34ME6EG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG/action/storage_attestation","attest_author":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG/action/author_attestation","sign_citation":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG/action/citation_signature","submit_replication":"https://pith.science/pith/QHCQ5LKLVRLVDS5LW7R34ME6EG/action/replication_record"}},"created_at":"2026-05-18T03:40:03.761733+00:00","updated_at":"2026-05-18T03:40:03.761733+00:00"}