Verifying Huppert's conjecture for \(^2G_2(q^2)\).
type: Item
instance of: scholarly article
title: Verifying Huppert's conjecture for \(^2G_2(q^2)\).
zbMATH Open document ID: 1257.20009
author: T. P. Wakefield
published in: Algebras and Representation Theory
publication date: 2012-07-10T00:00:00Z
review text: Let \(\text{cd}(G)\) denote the set of character degrees of a finite group \(G\). Then Huppert's conjecture states that if \(H\) is a finite group with \(\text{cd}(G)=\text{cd}(H)\), then \(G\) is isomorphic to the direct product of \(H\) by a group \(A\), where \(A\) is an Abelian group. This conjecture is proved for the Suzuki groups and a few of simple groups of Lie type and some other simple groups by \textit{B. Huppert} [in Ill. J. Math. 44, No. 4, 828-842 (2000; Zbl 0972.20006)]. In the paper under review the author proves the conjecture for the twisted Ree group \(^2G_2(q^2)\) for \(q^2=3^{2m+1}\), \(m\) greater or equal to \(1\).
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 6054169
zbMATH Keywords: sets of character degrees
zbMATH Keywords: finite simple groups
zbMATH Keywords: Huppert conjecture
zbMATH Keywords: irreducible characters
zbMATH Keywords: simple groups of Lie type
zbMATH Keywords: twisted Ree groups
MaRDI profile type: Publication
full work available at URL: s10468-009-9206-x
OpenAlex ID: W2035177596
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DOI: 10.1007/S10468-009-9206-X
description: scientific article; zbMATH DE number 6054169