## Abstract

We consider the question of determining whether or not a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for constructing candidate right-angled Coxeter presentations for a given group or proving that one cannot exist. We apply this process to a number of examples. Our new results imply several known results as corollaries. In particular, we provide an elementary proof of rigidity of the defining graph for a right-angled Coxeter group, and we recover an existing result stating that if Γ satisfies a particular graph condition (called no SILs), then Aut^{0}.(W _{Γ}) is a right-angled Coxeter group.

Original language | English |
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Pages (from-to) | 41-77 |

Number of pages | 37 |

Journal | Pacific Journal of Mathematics |

Volume | 284 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |