Reflection subgroups of Coxeter groups

Details Reflection subgroups of Coxeter groups Reflection subgroups of Coxeter groups

2007-05-03

arxiv.org/abs/0705.0426v3

Trans. Amer. Math. Soc. 362 (2010), 847--858

Mathematics

Group Theory

v3: the proofs of Theorem 1 and Lemma 5 are corrected, an example added. 13 pages

Scientific paper

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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