{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IOA7F3YTI37A7YLHYON2ZPOGLK","short_pith_number":"pith:IOA7F3YT","schema_version":"1.0","canonical_sha256":"4381f2ef1346fe0fe167c39bacbdc65ab557e585dd9aecb3d8ffced1a94231cb","source":{"kind":"arxiv","id":"1310.7214","version":1},"attestation_state":"computed","paper":{"title":"From the Poincar\\'e Theorem to generators of the unit group of integral group rings of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Ann Kiefer, Anotnio Calixto Souza Filho, Antonio de Andrade e Silva, Eric Jespers, Stanley Orlando Juriaans","submitted_at":"2013-10-27T17:03:09Z","abstract_excerpt":"We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\\mathbb{Q} G$ does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre $\\mathbb{Q}$. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy imple"},"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":"1310.7214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T17:03:09Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"2f356cfe6e7043838b116cee29a70d06eb40f8058d6ad1a1580558899ae3bc6b","abstract_canon_sha256":"85e639026264f94903d160e8c3fc5b88a629e838edbc528e7ac3e14ff7d863be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:45.928909Z","signature_b64":"jsPWrsmyuHM8L/jzwGrp+4JZsV5SEqz9y2lXFapSsRjL2SzGGo/3Wu58JNagfXlV3mG66MMLReN4SFE4TWapBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4381f2ef1346fe0fe167c39bacbdc65ab557e585dd9aecb3d8ffced1a94231cb","last_reissued_at":"2026-05-18T03:08:45.928421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:45.928421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From the Poincar\\'e Theorem to generators of the unit group of integral group rings of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Ann Kiefer, Anotnio Calixto Souza Filho, Antonio de Andrade e Silva, Eric Jespers, Stanley Orlando Juriaans","submitted_at":"2013-10-27T17:03:09Z","abstract_excerpt":"We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\\mathbb{Q} G$ does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre $\\mathbb{Q}$. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy imple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7214","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":"1310.7214","created_at":"2026-05-18T03:08:45.928494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.7214v1","created_at":"2026-05-18T03:08:45.928494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7214","created_at":"2026-05-18T03:08:45.928494+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOA7F3YTI37A","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOA7F3YTI37A7YLH","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOA7F3YT","created_at":"2026-05-18T12:27:46.883200+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/IOA7F3YTI37A7YLHYON2ZPOGLK","json":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK.json","graph_json":"https://pith.science/api/pith-number/IOA7F3YTI37A7YLHYON2ZPOGLK/graph.json","events_json":"https://pith.science/api/pith-number/IOA7F3YTI37A7YLHYON2ZPOGLK/events.json","paper":"https://pith.science/paper/IOA7F3YT"},"agent_actions":{"view_html":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK","download_json":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK.json","view_paper":"https://pith.science/paper/IOA7F3YT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.7214&json=true","fetch_graph":"https://pith.science/api/pith-number/IOA7F3YTI37A7YLHYON2ZPOGLK/graph.json","fetch_events":"https://pith.science/api/pith-number/IOA7F3YTI37A7YLHYON2ZPOGLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK/action/storage_attestation","attest_author":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK/action/author_attestation","sign_citation":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK/action/citation_signature","submit_replication":"https://pith.science/pith/IOA7F3YTI37A7YLHYON2ZPOGLK/action/replication_record"}},"created_at":"2026-05-18T03:08:45.928494+00:00","updated_at":"2026-05-18T03:08:45.928494+00:00"}