Spherical and affine Artin groups, finite quotients, and the isomorphism problem

Abstract

We compute the smallest non-abelian quotients of spherical and affine Artin groups. Usually, these are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter groups. As applications, we deduce that two affine Artin groups are isomorphic if and only if their Coxeter diagrams are isomorphic and that irreducible spherical Artin groups are distinguished from each other by their finite quotient groups.

arXiv commentv3. 44 pages, title changed and new result added; v2. 42 pages, minor changes; v1. 42 pages, preliminary version