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December 2007 On the extension of $\mathrm {G}_{2}(3^{2n+1})$ by the exceptional graph automorphism
Olivier Brunat
Osaka J. Math. 44(4): 973-1023 (December 2007).

Abstract

The main aim of this paper is to compute the character table of $\mathrm{G}_{2}(3^{2n+1})\rtimes\langle \sigma \rangle$, where $\sigma$ is the graph automorphism of $\mathrm{G}_{2}(3^{2n+1})$ such that the fixed-point subgroup $\mathrm{G}_{2}(3^{2n+1})^{\sigma}$ is the Ree group of type $\mathrm{G}_{2}$. As a consequence we explicitly construct a perfect isometry between the principal $p$-blocks of $\mathrm{G}_{2}(3^{2n+1})^{\sigma}$ and $\mathrm{G}_{2}(3^{2n+1})\rtimes\langle \sigma \rangle$ for prime numbers dividing $q^2-q+1$.

Citation

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Olivier Brunat. "On the extension of $\mathrm {G}_{2}(3^{2n+1})$ by the exceptional graph automorphism." Osaka J. Math. 44 (4) 973 - 1023, December 2007.

Information

Published: December 2007
First available in Project Euclid: 7 January 2008

zbMATH: 1138.20011
MathSciNet: MR2383821

Subjects:
Primary: 20C15 , 20C33

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics

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Vol.44 • No. 4 • December 2007
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