Geodesic
On generation of the groups $GL_n(\mathbb{Z})$ and $PGL_n(\mathbb{Z})$ by three involutions, two of which commute
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 413-419.

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It is proved that the general linear group $GL_n(\mathbb{Z})$ (its projective image $PGL_n(\mathbb{Z})$ respectively) over the ring of integers $\mathbb{Z}$ is generated by three involutions, two of which commute, if and only if $n\geqslant 5$ (if $n=2$ and $n \geqslant 5$ respectively).
Keywords: general linear group, ring of integers, generating triples of involutions. 
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Irina A. Markovskaya; Yakov N. Nuzhin. On generation of the groups $GL_n(\mathbb{Z})$ and $PGL_n(\mathbb{Z})$ by three involutions, two of which commute. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 413-419. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a0/

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