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arXiv · 2609.21946

Finite Quotients of Right-angled Artin Groups

Zihao Liu
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Abstract

We prove that right-angled Artin groups (RAAGs) are profinitely rigid relative to the class of Artin groups. More precisely, if $A_Γ$ is an arbitrary Artin group and $A_Λ$ is a right-angled Artin group such that their profinite completions are isomorphic, i.e., $\widehat{A_Γ}\cong\widehat{A_Λ},$ then $Γ$ is right-angled and $Γ\congΛ$ as labeled graphs. The proof combines the structure of pro-$p$ completions of Artin groups with finite Coxeter quotients to recover the defining graph.

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Zihao Liu. 2026-09-18. Finite Quotients of Right-angled Artin Groups. https://arxiv.org/abs/2609.21946

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