On some discrete reflection groups and congruence subgroups
نویسندگان
چکیده
منابع مشابه
On finite index reflection subgroups of discrete reflection groups
Let G be a discrete group generated by reflections in hyperbolic or Euclidean space, and H ⊂ G be a finite index subgroup generated by reflections. Suppose that the fundamental chamber of G is a finite volume polytope with k facets. In this paper, we prove that the fundamental chamber of H has at least k facets. 1. Let X be hyperbolic space H, Euclidean space E or spherical space S . A polytope...
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We use geometry of Davis complex of a Coxeter group to investigate finite index reflection subgroups of Coxeter groups. The main result is the following: if G is an infinite indecomposable Coxeter group and H ⊂ G is a finite index reflection subgroup then the rank of H is not less than the rank of G. This generalizes results of [7]. We also describe some properties of the nerves of the group an...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1991
ISSN: 0386-2194
DOI: 10.3792/pjaa.67.125