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We prove the Zassenhaus Conjecture for the groups $\\text{SL}(2,p)$ and $\\text{SL}(2,p^2)$ with $p$ a prime number. This is the first infinite family of non-solvable groups for which the Zassenhaus Conjecture has been proved. We also prove that if $G=\\text{SL}(2,p^f)$, with $f$ arbitrary and $u$ is a torsion unit of $\\mathbb{Z}G$ with augmentation $1$ and order coprime with $p$"},"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":"1803.05342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-14T15:09:40Z","cross_cats_sorted":[],"title_canon_sha256":"ed5d835ad0cd3c2acdb4b76274d12a644c4960d61ce265f2ddd0cd4302098d76","abstract_canon_sha256":"88fcb4b9e57b9d8d95bce119ca16c477a050310af7c16df4d3b855c06bbda941"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:45.570866Z","signature_b64":"910M+REnRBiHWfYS0zm7NApiuCoBGSHZLAArpRQqWgp6oH/cby0Y4e0jLrVvag/53ujkl2sFfP9QPw3QY428Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89b8d4d7d378c2e88faf3caeb1e5f35c73a50da6c0912c21849faa087a06d608","last_reissued_at":"2026-05-18T00:18:45.570219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:45.570219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zassenhaus Conjecture on torsion units holds for $\\text{SL}(2,p)$ and $\\text{SL}(2,p^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Angel del R\\'io, Mariano Serrano","submitted_at":"2018-03-14T15:09:40Z","abstract_excerpt":"H.J. Zassenhaus conjectured that any unit of finite order and augmentation $1$ in the integral group ring $\\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra $\\mathbb{Q}G$ to an element of $G$. We prove the Zassenhaus Conjecture for the groups $\\text{SL}(2,p)$ and $\\text{SL}(2,p^2)$ with $p$ a prime number. This is the first infinite family of non-solvable groups for which the Zassenhaus Conjecture has been proved. We also prove that if $G=\\text{SL}(2,p^f)$, with $f$ arbitrary and $u$ is a torsion unit of $\\mathbb{Z}G$ with augmentation $1$ and order coprime with $p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05342","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":"1803.05342","created_at":"2026-05-18T00:18:45.570335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05342v2","created_at":"2026-05-18T00:18:45.570335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05342","created_at":"2026-05-18T00:18:45.570335+00:00"},{"alias_kind":"pith_short_12","alias_value":"RG4NJV6TPDBO","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RG4NJV6TPDBORD5P","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RG4NJV6T","created_at":"2026-05-18T12:32:50.500415+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/RG4NJV6TPDBORD5PHSXLDZPTLR","json":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR.json","graph_json":"https://pith.science/api/pith-number/RG4NJV6TPDBORD5PHSXLDZPTLR/graph.json","events_json":"https://pith.science/api/pith-number/RG4NJV6TPDBORD5PHSXLDZPTLR/events.json","paper":"https://pith.science/paper/RG4NJV6T"},"agent_actions":{"view_html":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR","download_json":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR.json","view_paper":"https://pith.science/paper/RG4NJV6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05342&json=true","fetch_graph":"https://pith.science/api/pith-number/RG4NJV6TPDBORD5PHSXLDZPTLR/graph.json","fetch_events":"https://pith.science/api/pith-number/RG4NJV6TPDBORD5PHSXLDZPTLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR/action/storage_attestation","attest_author":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR/action/author_attestation","sign_citation":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR/action/citation_signature","submit_replication":"https://pith.science/pith/RG4NJV6TPDBORD5PHSXLDZPTLR/action/replication_record"}},"created_at":"2026-05-18T00:18:45.570335+00:00","updated_at":"2026-05-18T00:18:45.570335+00:00"}