{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WCVCVDPS3NRVICLS4NQRQCK2YD","short_pith_number":"pith:WCVCVDPS","schema_version":"1.0","canonical_sha256":"b0aa2a8df2db63540972e36118095ac0cb3f93ce22c439a20ca54e4023436880","source":{"kind":"arxiv","id":"1205.2498","version":1},"attestation_state":"computed","paper":{"title":"On the intersection of the $\\cal F$-maximal subgroups and the generalized ${\\cal F}$-hypercentre of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Wenbin Guo","submitted_at":"2012-05-11T12:21:50Z","abstract_excerpt":"Let $\\cal F$ be a class of groups. A chief factor $H/K$ of a group $G$ is called \\emph{${\\cal F}$-central in $G$} provided $(H/K)\\rtimes (G/C_{G}(H/K)) \\in {\\cal F}$. We write $Z_{\\pi{\\cal F}}(G)$ to denote the product of all normal subgroups of $G$ whose $G$-chief factors of order divisible by at least one prime in $\\pi$ are $\\cal F$-central. We call $Z_{\\pi{\\cal F}}(G)$ the $\\pi{\\cal F}$-hypercentre of $G$. A subgroup $U$ of a group $G$ is called \\emph{$\\cal F$-maximal} in $G$ provided that (a) $U\\in {\\cal F}$, and (b) if $U\\leq V\\leq G$ and $V\\in {\\cal F}$, then $U=V$.\n  In this paper we st"},"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":"1205.2498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-05-11T12:21:50Z","cross_cats_sorted":[],"title_canon_sha256":"a683d33e33614eba1512164e4f2b8def3cc108380ae5910c5cd73b23affe48b9","abstract_canon_sha256":"280ee3f13f15f62c36ef6f432c82645f5aea1c19a3e654e14d0f2ea58b214ce3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:23.862172Z","signature_b64":"Lbofra+NKuFxPUMCiDtJX8BtSD8WZbO7ZRWYc8eX7js9RGo/rVTyjG9+FxNyKxVRRpEwuEyqTzyx6nka0BSnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0aa2a8df2db63540972e36118095ac0cb3f93ce22c439a20ca54e4023436880","last_reissued_at":"2026-05-18T03:55:23.861586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:23.861586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the intersection of the $\\cal F$-maximal subgroups and the generalized ${\\cal F}$-hypercentre of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Wenbin Guo","submitted_at":"2012-05-11T12:21:50Z","abstract_excerpt":"Let $\\cal F$ be a class of groups. A chief factor $H/K$ of a group $G$ is called \\emph{${\\cal F}$-central in $G$} provided $(H/K)\\rtimes (G/C_{G}(H/K)) \\in {\\cal F}$. We write $Z_{\\pi{\\cal F}}(G)$ to denote the product of all normal subgroups of $G$ whose $G$-chief factors of order divisible by at least one prime in $\\pi$ are $\\cal F$-central. We call $Z_{\\pi{\\cal F}}(G)$ the $\\pi{\\cal F}$-hypercentre of $G$. A subgroup $U$ of a group $G$ is called \\emph{$\\cal F$-maximal} in $G$ provided that (a) $U\\in {\\cal F}$, and (b) if $U\\leq V\\leq G$ and $V\\in {\\cal F}$, then $U=V$.\n  In this paper we st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2498","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":"1205.2498","created_at":"2026-05-18T03:55:23.861694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.2498v1","created_at":"2026-05-18T03:55:23.861694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2498","created_at":"2026-05-18T03:55:23.861694+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCVCVDPS3NRV","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCVCVDPS3NRVICLS","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCVCVDPS","created_at":"2026-05-18T12:27:25.539911+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/WCVCVDPS3NRVICLS4NQRQCK2YD","json":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD.json","graph_json":"https://pith.science/api/pith-number/WCVCVDPS3NRVICLS4NQRQCK2YD/graph.json","events_json":"https://pith.science/api/pith-number/WCVCVDPS3NRVICLS4NQRQCK2YD/events.json","paper":"https://pith.science/paper/WCVCVDPS"},"agent_actions":{"view_html":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD","download_json":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD.json","view_paper":"https://pith.science/paper/WCVCVDPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.2498&json=true","fetch_graph":"https://pith.science/api/pith-number/WCVCVDPS3NRVICLS4NQRQCK2YD/graph.json","fetch_events":"https://pith.science/api/pith-number/WCVCVDPS3NRVICLS4NQRQCK2YD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD/action/storage_attestation","attest_author":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD/action/author_attestation","sign_citation":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD/action/citation_signature","submit_replication":"https://pith.science/pith/WCVCVDPS3NRVICLS4NQRQCK2YD/action/replication_record"}},"created_at":"2026-05-18T03:55:23.861694+00:00","updated_at":"2026-05-18T03:55:23.861694+00:00"}