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Paper detail

A characterization of finitely generated reflection subgroups of Coxeter groups orthogonal to a reflection

Given a reflection $r$ in a Coxeter group $W$ (possibly of infinite rank), we consider the subgroup of $W$ generated by the reflections in $W$ having (-1)-eigenvectors orthogonal to the (-1)-eigenvector of $r$. In this paper, we determine completely when this subgroup is finitely generated, by using preceding results on centralizers of reflections. This result provides a new and naturally constructed example of a family of non-finitely generated subgroups of finitely generated groups.

preprint2012arXivOpen access
Koji Nuida
math.GR
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Koji Nuida

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