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 Lobachevsky 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 Lobachevsky space and fixed degree of the ground field over Q.
Figures: 6. Tables: 1. Bibliography: 19 titles.