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April 2020 Extending Huppert’s conjecture to almost simple groups of Lie type
Farrokh Shirjian, Ali Iranmanesh
Illinois J. Math. 64(1): 49-69 (April 2020). DOI: 10.1215/00192082-8165590

Abstract

Let G be a finite group and cd(G) be the set of all irreducible complex character degrees of G without multiplicities. The aim of this paper is to propose an extension of Huppert’s conjecture from non-Abelian simple groups to almost simple groups of Lie type. Indeed, we conjecture that if H is an almost simple group of Lie type with cd(G)=cd(H), then there exists an Abelian normal subgroup A of G such that G/AH. It is furthermore shown that G is not necessarily the direct product of H and A. In view of Huppert’s conjecture, we also show that the converse implication does not necessarily hold for almost simple groups. Finally, in support of this conjecture, we will confirm it for projective general linear and unitary groups of dimension 3.

Citation

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Farrokh Shirjian. Ali Iranmanesh. "Extending Huppert’s conjecture to almost simple groups of Lie type." Illinois J. Math. 64 (1) 49 - 69, April 2020. https://doi.org/10.1215/00192082-8165590

Information

Received: 20 December 2018; Revised: 23 October 2019; Published: April 2020
First available in Project Euclid: 6 March 2020

zbMATH: 07179189
MathSciNet: MR4072641
Digital Object Identifier: 10.1215/00192082-8165590

Subjects:
Primary: 20C15
Secondary: 20C33 , 20G40

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 1 • April 2020
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