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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(V_{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> are generated by 4 involutions, generalising a classical result of Higman for Thompson’s group <i>V</i>.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月11日

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  • Samuel M. Corson,
  • Sam Hughes,
  • Philip Möller,
  • Olga Varghese

摘要

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 \(V_{n}\) V n are generated by 4 involutions, generalising a classical result of Higman for Thompson’s group V.