On reflections in Coxeter groups commuting with a reflection

Abstract

We consider the subgroup of an arbitrary Coxeter group generated by the reflections which commute with a given reflection. We determine completely for which case this subgroup is finitely generated. This result provides new uniform examples of non-finitely generated subgroups in finitely generated groups.

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Cite this paper

@inproceedings{Nuida2006OnRI, title={On reflections in Coxeter groups commuting with a reflection}, author={Koji Nuida and Vinay V. Deodhar}, year={2006} }