Reflection subgroups of Coxeter groups
Group Theory
2019-10-25 v3
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 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.
Cite
@article{arxiv.0705.0426,
title = {Reflection subgroups of Coxeter groups},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:0705.0426},
year = {2019}
}