On a theorem of Artin, II

Details On a theorem of Artin, II On a theorem of Artin, II

2004-11-09

arxiv.org/abs/math/0411193v1

Mathematics

Group Theory

Scientific paper

This paper is a sequel of [A.M. Cohen, L. Paris, {\it On a theorem of Artin}, J. Group Theory {\bf 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 $\mu: A \to W$. We determine the homomorphisms $\f: A \to W$ that verify $\Im \f \cdot Z(W)= W$, 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.

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