Geodesic
The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension
Izvestiya. Mathematics , Tome 28 (1987) no. 2, pp. 401-411

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The following theorem is proved: There are no discrete groups generated by reflections with fundamental polyhedron of finite volume in Lobachevskii space of dimension $995$. Bibliography: 8 titles. 
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     author = {M. N. Prokhorov},
     title = {The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in {Lobachevskii} space of large dimension},
     journal = {Izvestiya. Mathematics },
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M. N. Prokhorov. The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension. Izvestiya. Mathematics , Tome 28 (1987) no. 2, pp. 401-411. http://geodesic.mathdoc.fr/item/IM2_1987_28_2_a6/