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

Key Points

• To explore the profinite properties of right-angled Coxeter groups and their rigidity among various group classes.
• Proved profinite rigidity of right-angled Coxeter groups among all Coxeter groups.
• Exhibited right-angled Coxeter groups with infinite profinite genus within finitely generated residually finite groups.
• Established results for profinite rigidity in graph products of finite groups.
• Demonstrated that Higman–Thompson groups are generated by 4 involutions.
• Right-angled Coxeter groups are proven to be profinitely rigid within Coxeter groups.
• Certain right-angled Coxeter groups have been shown to possess infinite profinite genus.
• Profinite rigidity results obtained for graph products of finite groups extend prior findings.
• Higman–Thompson groups are generated by four involutions, adding depth to their characterization.