Groups generated by discrete sets of reflections

It is proved that a centroaffine group G generated by a discrete G-invariant set of reflections of Euclidean space E ³ is discrete. Affine nondiscrete groups generated by reflections in E ³ but containing only discrete sets of reflections are constructed. Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 59–66, 1991.