Recognizing right-angled Coxeter groups using involutions

Charles Cunningham, Andy Eisenberg, Adam Piggott, Kim Ruane

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 Aut0.(W Γ) is a right-angled Coxeter group.

Original languageEnglish
Pages (from-to)41-77
Number of pages37
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 2016
Externally publishedYes


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