{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OJQOBGBHNE47AVANAMQAV4DW42","short_pith_number":"pith:OJQOBGBH","schema_version":"1.0","canonical_sha256":"7260e098276939f0540d03200af076e6bed1273c42eb8a3ef7843c91a432bf41","source":{"kind":"arxiv","id":"1202.2385","version":1},"attestation_state":"computed","paper":{"title":"Some Groups with Computable Chermak-Delgado Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ben Brewster, Elizabeth Wilcox","submitted_at":"2012-02-10T23:21:06Z","abstract_excerpt":"Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the collection of all subgroups of G with maximal Chermak-Delgado measure, denoted CD(G), is a sublattice of the lattice of all subgroups of G. In this paper we note that the members of CD(G) are subnormal in G and determine the Chermak-Delgado lattice of direct products. We additionally describe the lattice for certain kinds of wreath products and examine the behavior"},"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":"1202.2385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-10T23:21:06Z","cross_cats_sorted":[],"title_canon_sha256":"81818e338c5b8db3542ff50ba0e2c18bad0119f969e3668ff39e4d85dcb08c8a","abstract_canon_sha256":"005d2d1b260a07fe5937abb80ddbd6c754c1d612846f1bf1f3a7878f8d698f7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:05.947980Z","signature_b64":"bUExjL5b4qmYIqUnIejQEj+rqg4cfTfvbbYc4Pkjz6NVUG8P3JOJy9N8I2a1CCAifR5ooGTtORFDB6b1b/PsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7260e098276939f0540d03200af076e6bed1273c42eb8a3ef7843c91a432bf41","last_reissued_at":"2026-05-18T02:47:05.947522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:05.947522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Groups with Computable Chermak-Delgado Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ben Brewster, Elizabeth Wilcox","submitted_at":"2012-02-10T23:21:06Z","abstract_excerpt":"Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the collection of all subgroups of G with maximal Chermak-Delgado measure, denoted CD(G), is a sublattice of the lattice of all subgroups of G. In this paper we note that the members of CD(G) are subnormal in G and determine the Chermak-Delgado lattice of direct products. We additionally describe the lattice for certain kinds of wreath products and examine the behavior"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2385","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":"1202.2385","created_at":"2026-05-18T02:47:05.947596+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2385v1","created_at":"2026-05-18T02:47:05.947596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2385","created_at":"2026-05-18T02:47:05.947596+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJQOBGBHNE47","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJQOBGBHNE47AVAN","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJQOBGBH","created_at":"2026-05-18T12:27:16.716162+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/OJQOBGBHNE47AVANAMQAV4DW42","json":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42.json","graph_json":"https://pith.science/api/pith-number/OJQOBGBHNE47AVANAMQAV4DW42/graph.json","events_json":"https://pith.science/api/pith-number/OJQOBGBHNE47AVANAMQAV4DW42/events.json","paper":"https://pith.science/paper/OJQOBGBH"},"agent_actions":{"view_html":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42","download_json":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42.json","view_paper":"https://pith.science/paper/OJQOBGBH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2385&json=true","fetch_graph":"https://pith.science/api/pith-number/OJQOBGBHNE47AVANAMQAV4DW42/graph.json","fetch_events":"https://pith.science/api/pith-number/OJQOBGBHNE47AVANAMQAV4DW42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42/action/storage_attestation","attest_author":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42/action/author_attestation","sign_citation":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42/action/citation_signature","submit_replication":"https://pith.science/pith/OJQOBGBHNE47AVANAMQAV4DW42/action/replication_record"}},"created_at":"2026-05-18T02:47:05.947596+00:00","updated_at":"2026-05-18T02:47:05.947596+00:00"}