{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VETXYVD72YHNH6APMOOR4CO3BD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"04e80ee3e66caaf4722b923cbe4470a2984a4497d030fb93b112a6ebdbcdcb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-01T04:09:05Z","title_canon_sha256":"b540daf3e4f29f57de77e04b41b3f44679c6f883506926fcef1aa9055d54d8d2"},"schema_version":"1.0","source":{"id":"1709.00148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00148","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00148v1","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00148","created_at":"2026-05-18T00:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"VETXYVD72YHN","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VETXYVD72YHNH6AP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VETXYVD7","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:c93917331550ca91e0a381904d38993376506679a4308457c036cb6cbf7e07bd","target":"graph","created_at":"2026-05-18T00:36:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Denote by $\\nu_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $\\nu_p(H)\\leq\\nu_p(G)$ for $H\\leq G$, however $\\nu_p(H)$ does not divide $\\nu_p(G)$ in general. In this paper we reduce the question whether $\\nu_p(H)$ divides $\\nu_p(G)$ for every $H\\leq G$ to almost simple groups. This result substantially generalizes the previous result by G. Navarro and also provides an alternative proof for the Navarro theorem.","authors_text":"Evgeny Vdovin, Wenbin Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-01T04:09:05Z","title":"Number of Sylow subgroups in finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00148","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:02e25cf52d2d5cc5df8d608e729d6203c1eccb84e0674d6587a148388df55d68","target":"record","created_at":"2026-05-18T00:36:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"04e80ee3e66caaf4722b923cbe4470a2984a4497d030fb93b112a6ebdbcdcb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-01T04:09:05Z","title_canon_sha256":"b540daf3e4f29f57de77e04b41b3f44679c6f883506926fcef1aa9055d54d8d2"},"schema_version":"1.0","source":{"id":"1709.00148","kind":"arxiv","version":1}},"canonical_sha256":"a9277c547fd60ed3f80f639d1e09db08f2d88dc8cf94ee888920754c1f8a2363","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9277c547fd60ed3f80f639d1e09db08f2d88dc8cf94ee888920754c1f8a2363","first_computed_at":"2026-05-18T00:36:13.262904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:13.262904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kC2K0UTd6EP4zX+wVFPkrVDEr/v8xuSZEZfj/3AVhx3Lq+Yzqbl9o/nXehoIjGXxgF0/u9d/StVtLcFEe5lHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:13.263532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02e25cf52d2d5cc5df8d608e729d6203c1eccb84e0674d6587a148388df55d68","sha256:c93917331550ca91e0a381904d38993376506679a4308457c036cb6cbf7e07bd"],"state_sha256":"9146e6818f39f4a261d2895115ce285cfc9d6c974b14d73eea474120777d4149"}