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Finite Quotients of Right-angled Artin Groups
Abstract
We prove that right-angled Artin groups (RAAGs) are profinitely rigid relative to the class of Artin groups. More precisely, if AΓ is an arbitrary Artin group and AΛ is a right-angled Artin group such that their profinite completions are isomorphic, i.e., AΓ̂≅AΛ̂, then Γ is right-angled and Γ≅Λ as labeled graphs. The proof combines the structure of pro-p completions of Artin groups with finite Coxeter quotients to recover the defining graph.
Related
- Right angled Artin groups and partial commutation, old and new
- Quasiisometric embeddings of right-angled Artin groups into products
- Quasi-Projectivity of Weighted Right-Angled Artin Groups
- Quasiisometric embeddings between right-angled Artin groups: flexibility
- Quasiisometric embeddings between right-angled Artin groups: rigidity
BibTeX
@misc{liu2026finite,
title = {{Finite Quotients of Right-angled Artin Groups}},
author = {Zihao Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21946},
eprint = {2609.21946},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21946},
}
RIS
TY - UNPB
TI - Finite Quotients of Right-angled Artin Groups
AU - Zihao Liu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21946
UR - https://arxiv.org/abs/2609.21946
AB - 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., A_Γ̂≅A_Λ̂, then Γ is right-angled and Γ≅Λ as labeled graphs. The proof combines the structure of pro-p completions of Artin groups with finite Coxeter quotients to recover the defining graph.
ER -