Irreducible \((2,3,7)\)-subgroups of \(\text{PGL}_n(\mathbb{F})\), \(n\leqslant 7\). II.
type: Item
instance of: scholarly article
title: Irreducible \((2,3,7)\)-subgroups of \(\text{PGL}_n(\mathbb{F})\), \(n\leqslant 7\). II.
zbMATH Open document ID: 1180.20030
published in: Journal of Algebra
publication date: 2009-06-17T00:00:00Z
review text: Let \(\text{GL}_n(F)\) denote the general linear group in dimension \(n\) over an algebraically closed field \(F\) of characteristic \(p\geq 0\). Let \(x,y\in\text{GL}_n(F)\) and \(z=xy\). The sequence \((x,y,z)\) is called a \((2,3,7)\)-triple if \(x^2=y^3=z^3=1\), and the triple is called irreducible if \(\langle x,y\rangle\) is an irreducible subgroup of \(\text{GL}_n(F)\). This paper is the continuation of the authors' research stated in part I [\textit{M. C. Tamburini} and \textit{M. Vsemirnov}, J. Algebra 300, No. 1, 339-362 (2006; Zbl 1102.20026)]. The main result of the present paper is the classification of all the non-rigid irreducible \((2,3,7)\)-triples \((x,y,z)\) in \(\text{GL}_7(F)\).
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20H20
zbMATH DE Number: 5565623
zbMATH Keywords: Hurwitz groups
zbMATH Keywords: projective general linear groups
zbMATH Keywords: \((2,3,7)\)-groups
zbMATH Keywords: Hurwitz generations
zbMATH Keywords: rigidity
zbMATH Keywords: irreducible subgroups
author: M. Chiara Tamburini
author: Maxim Vsemirnov
describes a project that uses: JanetOre
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.11.038
OpenAlex ID: W2119240466
cites work: The Magma algebra system. I: The user language
cites work: On non-Hurwitz groups and non-congruence subgroups of the modular group
cites work: On hurwitz groups of low rank
cites work: Q3222326
cites work: Hurwitz Groups and G2(q)
cites work: Representations, commutative algebra, and Hurwitz groups.
cites work: Matrices and cohomology
cites work: Irreducible \((2,3,7)\)-subgroups of \(\text{PGL}_n(\mathbb{F})\), \(n\leqslant 7\).
cites work: Groups \(G_2(p)\) as quotients of \((2,3,7;2p)\).
DOI: 10.1016/J.JALGEBRA.2008.11.038
description: scientific article; zbMATH DE number 5565623