Geodesic
Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 53-56.

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After results of the author (1980, 1981) and Vinberg (1981), the finiteness of the number of maximal arithmetic groups generated by reflections in Lobachevsky spaces remained unknown in dimensions $2\le n\le 9$ only. It was proved recently (2005) in dimension 2 by Long, Maclachlan and Reid and in dimension 3 by Agol. Here we use the results in dimensions 2 and 3 to prove the finiteness in all remaining dimensions $4\le n\le 9$. The methods of the author (1980, 1981) are more than sufficient for this using a very short and very simple argument. 
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V. V. Nikulin. Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces. Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 53-56. http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a3/

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