On a theorem of Artin. II

Abstract

This paper is a sequel to [A. M. Cohen and L. Paris. On a theorem of Artin. J. Group Theory 6 (2003), 421–441.]. 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 μ : A → W . We determine the homomorphisms φ : A → W that satisfy Im φ · 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.