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arXiv · 0705.0426

Reflection subgroups of Coxeter groups

Anna Felikson·Pavel Tumarkin
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Abstract

We use geometry of Davis complex of a Coxeter group to prove the following result: if G is an infinite indecomposable Coxeter group and $H\subset G$ is a finite index reflection subgroup then the rank of H is not less than the rank of G. This generalizes results of math/0305093. We also describe some properties of the nerves of the group and the subgroup in the case of equal ranks.

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Anna Felikson, Pavel Tumarkin. 2007-05-03. Reflection subgroups of Coxeter groups. https://doi.org/10.1090/s0002-9947-09-04859-4

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