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2015 Complex group algebras of the double covers of the symmetric and alternating groups
Christine Bessenrodt, Hung Nguyen, Jørn Olsson, Hung Tong-Viet
Algebra Number Theory 9(3): 601-628 (2015). DOI: 10.2140/ant.2015.9.601

Abstract

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 5 be an integer, G a finite group, and let Ân and Ŝn± denote the double covers of An and Sn, respectively. We prove that GÂn if and only if GÂn, and GŜn+Ŝn if and only if GŜn+ or Ŝn. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasisimple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.

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Christine Bessenrodt. Hung Nguyen. Jørn Olsson. Hung Tong-Viet. "Complex group algebras of the double covers of the symmetric and alternating groups." Algebra Number Theory 9 (3) 601 - 628, 2015. https://doi.org/10.2140/ant.2015.9.601

Information

Received: 19 May 2014; Revised: 13 January 2015; Accepted: 23 February 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1321.20011
MathSciNet: MR3340546
Digital Object Identifier: 10.2140/ant.2015.9.601

Subjects:
Primary: 20C30
Secondary: 20C15, 20C33

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.9 • No. 3 • 2015
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