Note on residual finiteness of Artin groups

Ruben Blasco-Garcia (1) , Arye Juhasz (2) , Luis Paris (3)

1 Departamento de matemáticas [Zaragoza]
2 TECHNION - Department of Mathematics
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Let $A$ be an Artin group. A partition $\mathcal{P}$ of the set of standard generators of $A$ is called admissible if, for all $X,Y \in \mathcal{P}, X \neq Y$, there is at most one pair $(s,t) \in X \times Y$ which has a relation. An admissible partition $\mathcal{P}$ determines a quotient Coxeter graph $\Gamma/\mathcal{P}$. We prove that, if $\Gamma/\mathcal{P}$ 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.

Domaines: Théorie des groupes [math.GR]

Ruben Blasco-Garcia, Arye Juhasz, Luis Paris. Note on residual finiteness of Artin groups. Journal of Group Theory, 2018, 21 (3), pp.531-537. ⟨10.1515/jgth-2017-0049⟩. ⟨hal-01592583⟩