Irreducible \((2,3,7)\)-subgroups of \(\text{PGL}_n(\mathbb{F})\), \(n\leqslant 7\). II.
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 \(\text{GL}_7(F)\).
scientific article; zbMATH DE number 5565623
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