Higman-Thompson groups and profinite properties of right-angled Coxeter groups

2023/09/12 by Corson, Samuel M., Hughes, Sam, Möller, Philip +1 · 1 citation
#20E18 #20E45 #20F65 #FOS: Mathematics #Group Theory (math.GR) #Primary: 20F55 #Secondary: 20E36

paper · doi:10.48550/arxiv.2309.06213

Abstract

We prove that every right-angled Coxeter group (RACG) is profinitely rigid amongst all Coxeter groups. On the other hand we exhibit RACGs which have infinite profinite genus amongst all finitely generated residually finite groups. We also establish profinite rigidity results for graph products of finite groups. Along the way we prove that the Higman-Thompson groups V_n are generated by 4 involutions, generalising a classical result of Higman for Thompson's group V.

Cited by

• The profinite genus of the groups ℤⁿ\rtimes C_p²

Related

• Profinite rigidity of affine Coxeter groups
• Profinite rigidity of affine Coxeter groups
• Quasi-isometric rigidity of a class of right-angled Coxeter groups
• Profinite properties of Coxeter groups
• Locally rigid right-angled Coxeter groups with Fuchsian ends in dimension 5