Geodesic
Is the group $\mathrm{SL}(6,\mathbb{Z})$ $(2,3)$-generated?
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 101-130

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The problem whether the group $\mathrm{SL}(6,\mathbb{Z})$ can be generated by an involution and an element of order three is considered. The problem is reduced to the question whether $\mathrm{SL}(6,\mathbb{Z})$ is generated by one of eight explicitly written pairs of matrices. 
@article{ZNSL_2006_330_a5,
     author = {M. A. Vsemirnov},
     title = {Is the group $\mathrm{SL}(6,\mathbb{Z})$ $(2,3)$-generated?},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--130},
     publisher = {mathdoc},
     volume = {330},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a5/}
}
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M. A. Vsemirnov. Is the group $\mathrm{SL}(6,\mathbb{Z})$ $(2,3)$-generated?. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 101-130. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a5/