Covers of D-Type Artin Groups

Abstract

We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group $A(T)$ is defined by a signed graph $T$. Then we find a certain quotient $G(T)$ according to the graph $T$, which also have a natural map onto $A(D_n)$. We prove that $G(T)$ is isomorphic to a semidirect product of a group $K^{(m,n)}$, with the Artin group $A(D_n)$, where $K^{(m,n)}$ depends only on the number $m$ of cycles and on the number $n$ of vertices of the graph $T$.