Recognizing Right-Angled Coxeter Groups Using Involutions

Abstract

We consider the question of determining whether 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 provide some first applications. In addition, we provide an elementary proof of rigidity of the defining graph for a right-angled Coxeter group. We also recover a result stating that if the defining graph contains no SILs, then Aut^0(W) is a right-angled Coxeter group.

43 pages, 13 figures

References in corpus (2)

• Embedability between right-angled Artin groups
• On the automorphisms of a graph product of abelian groups

Cited by in corpus (2)

• The Geometry of Outer Automorphism Groups of Universal Right-Angled Coxeter Groups
• Detecting a subclass of torsion-generated groups