{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GUZ3EUKR63PHTVO27B662U7GJN","short_pith_number":"pith:GUZ3EUKR","schema_version":"1.0","canonical_sha256":"3533b25151f6de79d5daf87ded53e64b7933868b6465bca45ef7e9f1e0ccf0ee","source":{"kind":"arxiv","id":"1801.06738","version":1},"attestation_state":"computed","paper":{"title":"Two classes of finite groups whose Chermak-Delgado lattice is a chain of length zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Marius T\\u{a}rn\\u{a}uceanu, Ryan McCulloch","submitted_at":"2018-01-20T23:06:07Z","abstract_excerpt":"It is an open question in the study of Chermak-Delgado lattices precisely which finite groups $G$ have the property that $CD(G)$ is a chain of length $0$. In this note, we determine two classes of groups with this property. We prove that if $G=AB$ is a finite group, where $A$ and $B$ are abelian subgroups of relatively prime orders with $A$ normal in $G$, then the Chermak-Delgado lattice of $G$ equals $\\{AC_B(A)\\}$, a strengthening of earlier known results."},"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":"1801.06738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-20T23:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"e1e956610522416e8c5ea00001a286c36aa763f0905f7b31ca1fc29f73601b71","abstract_canon_sha256":"b7bdfa538ab3ab5ebdf3808d0cf48aa8af4a9d92dbdbbceeb40c66a4e6643741"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:27.900177Z","signature_b64":"v/puK9hN304V2Mz3RL6doqWrGyR93FeWLmJSggKJSBcTXwCz3AyZ4781Ye0aYt0ZJOsv+AObcE7DxJOdkKXSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3533b25151f6de79d5daf87ded53e64b7933868b6465bca45ef7e9f1e0ccf0ee","last_reissued_at":"2026-05-18T00:25:27.899517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:27.899517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two classes of finite groups whose Chermak-Delgado lattice is a chain of length zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Marius T\\u{a}rn\\u{a}uceanu, Ryan McCulloch","submitted_at":"2018-01-20T23:06:07Z","abstract_excerpt":"It is an open question in the study of Chermak-Delgado lattices precisely which finite groups $G$ have the property that $CD(G)$ is a chain of length $0$. In this note, we determine two classes of groups with this property. We prove that if $G=AB$ is a finite group, where $A$ and $B$ are abelian subgroups of relatively prime orders with $A$ normal in $G$, then the Chermak-Delgado lattice of $G$ equals $\\{AC_B(A)\\}$, a strengthening of earlier known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06738","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":"1801.06738","created_at":"2026-05-18T00:25:27.899630+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.06738v1","created_at":"2026-05-18T00:25:27.899630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06738","created_at":"2026-05-18T00:25:27.899630+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUZ3EUKR63PH","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUZ3EUKR63PHTVO2","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUZ3EUKR","created_at":"2026-05-18T12:32:25.280505+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/GUZ3EUKR63PHTVO27B662U7GJN","json":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN.json","graph_json":"https://pith.science/api/pith-number/GUZ3EUKR63PHTVO27B662U7GJN/graph.json","events_json":"https://pith.science/api/pith-number/GUZ3EUKR63PHTVO27B662U7GJN/events.json","paper":"https://pith.science/paper/GUZ3EUKR"},"agent_actions":{"view_html":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN","download_json":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN.json","view_paper":"https://pith.science/paper/GUZ3EUKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.06738&json=true","fetch_graph":"https://pith.science/api/pith-number/GUZ3EUKR63PHTVO27B662U7GJN/graph.json","fetch_events":"https://pith.science/api/pith-number/GUZ3EUKR63PHTVO27B662U7GJN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN/action/storage_attestation","attest_author":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN/action/author_attestation","sign_citation":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN/action/citation_signature","submit_replication":"https://pith.science/pith/GUZ3EUKR63PHTVO27B662U7GJN/action/replication_record"}},"created_at":"2026-05-18T00:25:27.899630+00:00","updated_at":"2026-05-18T00:25:27.899630+00:00"}