Geodesic
On arithmetic groups generated by reflections in Lobachevskii spaces
Izvestiya. Mathematics , Tome 16 (1981) no. 3, pp. 573-601

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Using È.  B. Vinberg's arithmeticity criterion, the author defines the notion of the Galois lattice of a discrete arithmetic group generated by reflections in a Lobachevskii space. The author proves finiteness of the set of such lattices and, as a corollary, finiteness of the set of maximal discrete arithmetic groups generated by reflections for fixed dimension of the Lobachevskii space and fixed degree of the ground field over $\mathbf Q$. Bibliography: 19 titles. 
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     author = {V. V. Nikulin},
     title = {On arithmetic groups generated by reflections in {Lobachevskii} spaces},
     journal = {Izvestiya. Mathematics },
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     number = {3},
     year = {1981},
     language = {en},
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V. V. Nikulin. On arithmetic groups generated by reflections in Lobachevskii spaces. Izvestiya. Mathematics , Tome 16 (1981) no. 3, pp. 573-601. http://geodesic.mathdoc.fr/item/IM2_1981_16_3_a4/