{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UDTBQGE5F6CFWYHAW5VZUVPB3X","short_pith_number":"pith:UDTBQGE5","schema_version":"1.0","canonical_sha256":"a0e618189d2f845b60e0b76b9a55e1ddc4b61ac30a1bd385668bd3ac9e88ad40","source":{"kind":"arxiv","id":"1507.08951","version":1},"attestation_state":"computed","paper":{"title":"On finite groups with some primary subgroups satisfying partial $S$-$\\Pi$-property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wenbin Guo, Xiaoyu Chen, Yuemei Mao","submitted_at":"2015-07-31T17:19:32Z","abstract_excerpt":"A $p$-subgroup $H$ of a finite group $G$ is said to satisfy partial $S$-$\\Pi$-property in $G$ if $G$ has a chief series $\\Gamma_{G}: 1=G_{0}<G_{1}<\\cdots<G_{n}=G$ such that for every $G$-chief factor $G_{i}/G_{i-1}$ $(1\\leqslant i\\leqslant n)$ of $\\Gamma_{G}$, either $(H\\cap G_{i})G_{i-1}/G_{i-1}$ is a Sylow $p$-subgroup of $G_{i}/G_{i-1}$ or $|G/G_{i-1}: N_{G/G_{i-1}}((H\\cap G_{i})G_{i-1}/G_{i-1})|$ is a $p$-number. In this paper, we mainly investigate the structure of finite groups with some primary subgroups satisfying partial $S$-$\\Pi$-property."},"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":"1507.08951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-31T17:19:32Z","cross_cats_sorted":[],"title_canon_sha256":"70f8f6e3a02c2a287c24c15b81e03467b7d32a44a9901dd1a715ab0ebc9513f3","abstract_canon_sha256":"376e3493f5d74cc3fa076858a3db0fea169a124fc3e7769e9103885c89df210b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:02.539640Z","signature_b64":"sWBpOqCNGlHmD3k55SwLR8RG3bOPzlQLSzoUhQXEjIuX6/IzJ/dGRlfJVffQYco9eocnfnq4heiiAwomr4ykDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0e618189d2f845b60e0b76b9a55e1ddc4b61ac30a1bd385668bd3ac9e88ad40","last_reissued_at":"2026-05-18T01:36:02.539029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:02.539029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On finite groups with some primary subgroups satisfying partial $S$-$\\Pi$-property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wenbin Guo, Xiaoyu Chen, Yuemei Mao","submitted_at":"2015-07-31T17:19:32Z","abstract_excerpt":"A $p$-subgroup $H$ of a finite group $G$ is said to satisfy partial $S$-$\\Pi$-property in $G$ if $G$ has a chief series $\\Gamma_{G}: 1=G_{0}<G_{1}<\\cdots<G_{n}=G$ such that for every $G$-chief factor $G_{i}/G_{i-1}$ $(1\\leqslant i\\leqslant n)$ of $\\Gamma_{G}$, either $(H\\cap G_{i})G_{i-1}/G_{i-1}$ is a Sylow $p$-subgroup of $G_{i}/G_{i-1}$ or $|G/G_{i-1}: N_{G/G_{i-1}}((H\\cap G_{i})G_{i-1}/G_{i-1})|$ is a $p$-number. In this paper, we mainly investigate the structure of finite groups with some primary subgroups satisfying partial $S$-$\\Pi$-property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08951","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":"1507.08951","created_at":"2026-05-18T01:36:02.539132+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08951v1","created_at":"2026-05-18T01:36:02.539132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08951","created_at":"2026-05-18T01:36:02.539132+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDTBQGE5F6CF","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDTBQGE5F6CFWYHA","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDTBQGE5","created_at":"2026-05-18T12:29:44.643036+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/UDTBQGE5F6CFWYHAW5VZUVPB3X","json":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X.json","graph_json":"https://pith.science/api/pith-number/UDTBQGE5F6CFWYHAW5VZUVPB3X/graph.json","events_json":"https://pith.science/api/pith-number/UDTBQGE5F6CFWYHAW5VZUVPB3X/events.json","paper":"https://pith.science/paper/UDTBQGE5"},"agent_actions":{"view_html":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X","download_json":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X.json","view_paper":"https://pith.science/paper/UDTBQGE5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08951&json=true","fetch_graph":"https://pith.science/api/pith-number/UDTBQGE5F6CFWYHAW5VZUVPB3X/graph.json","fetch_events":"https://pith.science/api/pith-number/UDTBQGE5F6CFWYHAW5VZUVPB3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X/action/storage_attestation","attest_author":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X/action/author_attestation","sign_citation":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X/action/citation_signature","submit_replication":"https://pith.science/pith/UDTBQGE5F6CFWYHAW5VZUVPB3X/action/replication_record"}},"created_at":"2026-05-18T01:36:02.539132+00:00","updated_at":"2026-05-18T01:36:02.539132+00:00"}