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By Anna Felikson and Pavel Tumarkin


We use the geometry of the 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 earlier results of the authors (2004). We also describe the relationship between the nerves of the group and the subgroup in the case of equal rank

Year: 2009
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