On a theorem of Artin

Abstract

We determine the epimorphisms $A\to W$ from the Artin group $A$ of type $\Gamma$ onto the Coxeter group $W$ of type $\Gamma$, in case $\Gamma$ is an irreducible Coxeter graph of spherical type, and we prove that the kernel of the standard epimorphism is a characteristic subgroup of $A$. This generalizes an over 50 years old result of Artin.