On a theorem of Artin, II

Abstract

This paper is a sequel of [8]. Let A be an Artin group, let W be its associated Coxeter group, and let CA be its associated coloured Artin group, that is, the kernel of the standard epimorphism xi: A -> W. We determine the homomorphisms A -> W that verify Im' ¢ Z(W) = W, for A irreducible and of spherical type, and we prove that CA is a characteristic subgroup of A, if A is of spherical type but not necessarily irreducible.