Showing a limited preview of this publication:
Abstract
Let Γ be a finitely generated infinite group. Denote by K (Γ ) the FC-centre of Γ, i.e. the subgroup of all elements of Γ having only finitely many conjugates in Γ. Let QI(Γ ) denote the group of quasi-isometries of Γ with respect to a word metric. We prove that the natural homomorphism θΓ : Aut(Γ ) → QI(Γ ) is a monomorphism only if K (Γ ) equals the centre Z (Γ ) of Γ. The converse holds if K (Γ ) = Z (Γ ) is torsion-free. When K (Γ ) is finite we show that
:
Published Online: 2005-11-18
Published in Print: 2005-07-20
Walter de Gruyter GmbH & Co. KG
