Some groups whose reduced C*-algebras have stable rank one

It is proved that, for the following classes of groups, Gamma, the reduced group C*-algebra C-lambda*(Gamma) has stable rank 1: (i) hyperbolic groups which are either torsion-free and non-elementary or w hich are cocompact lattices in a real, noncompact, simple, connected Lie gr oup of real rank 1 having trivial center; (ii) amalgamated free products of groups, Gamma = G(1 *H) G(2), where H is finite and there is gamma is an element of Gamma such that gamma(-1) H gamm a boolean AND H = {1}. The proofs involve some analysis of the free semigroup property, which is o ne way of saying that a group r has an abundance of free sub-semigroups, an d of the l(2)-spectral radius property, which says that spectral radius of appropriate elements in C-lambda*(Gamma) may be computed with the 2-norm. ( C) Elsevier, Paris.