{"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 $\\SSS^-$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4388","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"}