2004/11/09 by Nuno Franco, Luis Paris, Franco, Nuno +1
Mathematics · #20F36 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20F36
paper · pdf · doi:10.48550/arxiv.math/0411193
arxiv created 2004/11/09 · openalex publication_date 2004/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 μ: A → W. We determine the homomorphisms \f: A → W that verify \Im \f ⋅ 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.