{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YNT623PKWTE57T7YSS7BCGGCBT","short_pith_number":"pith:YNT623PK","schema_version":"1.0","canonical_sha256":"c367ed6deab4c9dfcff894be1118c20ce1685dd8b3fea9697fb0ce5143863477","source":{"kind":"arxiv","id":"1803.07678","version":2},"attestation_state":"computed","paper":{"title":"Lagrange's Theorem For Hom-Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mohammad Hassanzadeh","submitted_at":"2018-03-20T22:18:46Z","abstract_excerpt":"Hom-groups are nonassociative generalizations of groups where the unitality and associativity are twisted by a map. We show that a Hom-group (G, {\\alpha}) is a pointed idempotent quasigroup (pique). We use Cayley table of quasigroups to introduce some examples of Hom-groups. Introducing the notions of Hom-subgroups and cosets we prove Lagrange's theorem for finite Hom-groups. This states that the order of any Hom-subgroup H of a finite Hom-group G divides the order of G. We linearize Hom-groups to obtain a class of nonassociative Hopf algebras called Hom-Hopf algebras. As an application of our"},"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":"1803.07678","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-20T22:18:46Z","cross_cats_sorted":[],"title_canon_sha256":"d6c58e7c0c8c6879d4e53d4aa52f8507a6fb3ec1504768a9e241d18e8a303dcd","abstract_canon_sha256":"5937fad4ddc7edde2ebf990eb47835837742cd177d33de2076f2281e18eaf2fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:52.901346Z","signature_b64":"Fwrq3ZdtE4oD1xlDGz5GPLKokAPWAuJsCvjrREWS90PMQTi6PWGmuEbTqpITzWUxsQv345LHKgMJI2607VBQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c367ed6deab4c9dfcff894be1118c20ce1685dd8b3fea9697fb0ce5143863477","last_reissued_at":"2026-05-17T23:58:52.900838Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:52.900838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrange's Theorem For Hom-Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mohammad Hassanzadeh","submitted_at":"2018-03-20T22:18:46Z","abstract_excerpt":"Hom-groups are nonassociative generalizations of groups where the unitality and associativity are twisted by a map. We show that a Hom-group (G, {\\alpha}) is a pointed idempotent quasigroup (pique). We use Cayley table of quasigroups to introduce some examples of Hom-groups. Introducing the notions of Hom-subgroups and cosets we prove Lagrange's theorem for finite Hom-groups. This states that the order of any Hom-subgroup H of a finite Hom-group G divides the order of G. We linearize Hom-groups to obtain a class of nonassociative Hopf algebras called Hom-Hopf algebras. As an application of our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07678","kind":"arxiv","version":2},"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":"1803.07678","created_at":"2026-05-17T23:58:52.900908+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.07678v2","created_at":"2026-05-17T23:58:52.900908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07678","created_at":"2026-05-17T23:58:52.900908+00:00"},{"alias_kind":"pith_short_12","alias_value":"YNT623PKWTE5","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YNT623PKWTE57T7Y","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YNT623PK","created_at":"2026-05-18T12:33:04.347982+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/YNT623PKWTE57T7YSS7BCGGCBT","json":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT.json","graph_json":"https://pith.science/api/pith-number/YNT623PKWTE57T7YSS7BCGGCBT/graph.json","events_json":"https://pith.science/api/pith-number/YNT623PKWTE57T7YSS7BCGGCBT/events.json","paper":"https://pith.science/paper/YNT623PK"},"agent_actions":{"view_html":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT","download_json":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT.json","view_paper":"https://pith.science/paper/YNT623PK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.07678&json=true","fetch_graph":"https://pith.science/api/pith-number/YNT623PKWTE57T7YSS7BCGGCBT/graph.json","fetch_events":"https://pith.science/api/pith-number/YNT623PKWTE57T7YSS7BCGGCBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT/action/storage_attestation","attest_author":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT/action/author_attestation","sign_citation":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT/action/citation_signature","submit_replication":"https://pith.science/pith/YNT623PKWTE57T7YSS7BCGGCBT/action/replication_record"}},"created_at":"2026-05-17T23:58:52.900908+00:00","updated_at":"2026-05-17T23:58:52.900908+00:00"}