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# Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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1435-4446
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Volume 21, Issue 3

# Note on the residual finiteness of Artin groups

Rubén Blasco-García
/ Arye Juhász
/ Luis Paris
Published Online: 2018-01-26 | DOI: https://doi.org/10.1515/jgth-2017-0049

## Abstract

Let A be an Artin group. A partition $\mathcal{𝒫}$ of the set of standard generators of A is called admissible if, for all $X,Y\in \mathcal{𝒫}$, $X\ne Y$, there is at most one pair $\left(s,t\right)\in X×Y$ which has a relation. An admissible partition $\mathcal{𝒫}$ determines a quotient Coxeter graph $\mathrm{\Gamma }/\mathcal{𝒫}$. We prove that, if $\mathrm{\Gamma }/\mathcal{𝒫}$ is either a forest or an even triangle free Coxeter graph and ${A}_{X}$ is residually finite for all $X\in \mathcal{𝒫}$, then A is residually finite.

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Revised: 2017-12-22

Published Online: 2018-01-26

Published in Print: 2018-05-01

The first named author was partially supported by Gobierno de Aragón, European Regional Development Funds, MTM2015-67781-P (MINECO/ FEDER) and by the Departamento de Industria e Innovación del Gobierno de Aragón and Fondo Social Europeo Phd grant.

Citation Information: Journal of Group Theory, Volume 21, Issue 3, Pages 531–537, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883,

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