{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6RBY2TPGC3UBQSDAEGCR7GAP7I","short_pith_number":"pith:6RBY2TPG","schema_version":"1.0","canonical_sha256":"f4438d4de616e818486021851f980ffa0f239d9839bfb9bbce01386334b92dfd","source":{"kind":"arxiv","id":"1701.02008","version":1},"attestation_state":"computed","paper":{"title":"On p-stability in groups and fusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Zalesski, L\\'aszl\\'o H\\'ethelyi, Magdolna Sz\\H{o}ke","submitted_at":"2017-01-08T19:49:25Z","abstract_excerpt":"The aim of this paper is to generalise the notion of p-stability to fusion systems. We study the question how Qd(p) is involved in finite simple groups. We show that with a single exception a simple group involving Qd(p) has a subgroup isomorphic to either Qd(p) or a central extension of it by a cyclic group of order p. We define p-stability for fusion systems, characterise some of its properties and prove a fusion theoretic version of Thomson's maximal subgroup theorem. We introduce the notion of section p-stability both for groups and fusion systems and prove a version of Glauberman's theore"},"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":"1701.02008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-08T19:49:25Z","cross_cats_sorted":[],"title_canon_sha256":"0dc2c47c2853bf9b63f5acea04a94f218fa3c54ae1e3ed12006c731278e17555","abstract_canon_sha256":"bad34ad2a29c620704508850443d49e879a06804d281a07f08420ebafa205d3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.852380Z","signature_b64":"4vqkvTXzeyz2yC3vrs9GrcO1hQqP/r25c3p/+XbDifmpiYCIS72T4ukti5XxWlIf/X5u+9CIIoT1YaeR3psyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4438d4de616e818486021851f980ffa0f239d9839bfb9bbce01386334b92dfd","last_reissued_at":"2026-05-18T00:53:12.851854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.851854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On p-stability in groups and fusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Zalesski, L\\'aszl\\'o H\\'ethelyi, Magdolna Sz\\H{o}ke","submitted_at":"2017-01-08T19:49:25Z","abstract_excerpt":"The aim of this paper is to generalise the notion of p-stability to fusion systems. We study the question how Qd(p) is involved in finite simple groups. We show that with a single exception a simple group involving Qd(p) has a subgroup isomorphic to either Qd(p) or a central extension of it by a cyclic group of order p. We define p-stability for fusion systems, characterise some of its properties and prove a fusion theoretic version of Thomson's maximal subgroup theorem. We introduce the notion of section p-stability both for groups and fusion systems and prove a version of Glauberman's theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02008","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":"1701.02008","created_at":"2026-05-18T00:53:12.851925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02008v1","created_at":"2026-05-18T00:53:12.851925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02008","created_at":"2026-05-18T00:53:12.851925+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RBY2TPGC3UB","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RBY2TPGC3UBQSDA","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RBY2TPG","created_at":"2026-05-18T12:31:03.183658+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/6RBY2TPGC3UBQSDAEGCR7GAP7I","json":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I.json","graph_json":"https://pith.science/api/pith-number/6RBY2TPGC3UBQSDAEGCR7GAP7I/graph.json","events_json":"https://pith.science/api/pith-number/6RBY2TPGC3UBQSDAEGCR7GAP7I/events.json","paper":"https://pith.science/paper/6RBY2TPG"},"agent_actions":{"view_html":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I","download_json":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I.json","view_paper":"https://pith.science/paper/6RBY2TPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02008&json=true","fetch_graph":"https://pith.science/api/pith-number/6RBY2TPGC3UBQSDAEGCR7GAP7I/graph.json","fetch_events":"https://pith.science/api/pith-number/6RBY2TPGC3UBQSDAEGCR7GAP7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I/action/storage_attestation","attest_author":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I/action/author_attestation","sign_citation":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I/action/citation_signature","submit_replication":"https://pith.science/pith/6RBY2TPGC3UBQSDAEGCR7GAP7I/action/replication_record"}},"created_at":"2026-05-18T00:53:12.851925+00:00","updated_at":"2026-05-18T00:53:12.851925+00:00"}