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To be more precise, let $n\\geq 5$ be an integer, $G$ a finite group, and let $\\AAA$ and $\\SSS^\\pm$ denote the double covers of $\\Al_n$ and $\\Sy_n$, respectively. We prove that $\\CC G\\cong \\CC \\AAA$ if and only if $G\\cong \\AAA$, and $\\CC G\\cong \\CC \\SSS^+\\cong\\CC\\SSS^-$ if and only if $G\\cong \\SSS^+$ or $\\SSS^-$. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to iso"},"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":"1308.4388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-20T19:26:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ceac44e9972d4bb7487591463f4c21e81bba01bbc426536e610fb6bb43ba6deb","abstract_canon_sha256":"99d695a1bdf444e6f778ddd789077028a16800b1f894071c46634b6bb3f04023"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.076358Z","signature_b64":"xPJtE03KeokVI6Cct54ilAeLTPel1lCxeSNk2TjYt+PZaW6L55X2TBcGvT/nW4cWxJUWgkctkzYIm4xTGvzeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e64e5cdfce536e1bd57d63d88d444701c4165ba92c41527ea062e43b8cd0889","last_reissued_at":"2026-05-18T01:22:25.075618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.075618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex group algebras of the double covers of the symmetric and alternating groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Christine Bessenrodt, Hung Ngoc Nguyen, Hung P. Tong-Viet, J{\\o}rn B. Olsson","submitted_at":"2013-08-20T19:26:06Z","abstract_excerpt":"We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\\geq 5$ be an integer, $G$ a finite group, and let $\\AAA$ and $\\SSS^\\pm$ denote the double covers of $\\Al_n$ and $\\Sy_n$, respectively. We prove that $\\CC G\\cong \\CC \\AAA$ if and only if $G\\cong \\AAA$, and $\\CC G\\cong \\CC \\SSS^+\\cong\\CC\\SSS^-$ if and only if $G\\cong \\SSS^+$ or $\\SSS^-$. 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