Groupes de Coxeter infinis non affines. (Infinite non affine Coxeter groups) (Q1084184)

Let (W,S) be an irreducible Coxeter system, where the set S of reflections is finite and contains at least two elements. The author proves that, if the group W is infinite and has no abelian subgroup of finite index, then W contains a nonabelian free subgroup. As a corollary it follows that the following properties of W are equivalent: (i) W is neither finite nor affine; (ii) W does not have polynomial growth; (iii) W has exponential growth; (iv) W is not amenable.