Geodesic
Some systems of generators of the~group $\operatorname{GL}(n,\mathbb Z)$ for $n\leqslant 5$
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 131-137

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It is proved geometrically that the groups $\operatorname{GL}(n,\mathbb Z)$, $0$, are generated by systems of generators of finite groups $G_n$ and, for each such $n$, one additional substitution $h(n)$. 
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     title = {Some systems of generators of the~group $\operatorname{GL}(n,\mathbb Z)$ for $n\leqslant 5$},
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A. Dress; S. S. Ryshkov. Some systems of generators of the~group $\operatorname{GL}(n,\mathbb Z)$ for $n\leqslant 5$. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 131-137. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a7/