Bounded automorphisms and quasi-isometries of finitely generated groups

2002/12/09 by Naolekar, Aniruddha C., Sankaran, Parameswaran
#20F28 #20F65 #20F67 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0212114

Abstract

Let G be any finitely generated infinite group. Denote by K(G) the FC-centre of G, i.e., the subgroup of all elements of G whose centralizers are of finite index in G. Let QI(G) denote the group of quasi-isometries of G with respect to word metric. We observe that the natural homomorphism from the group of automorphisms of G to QI(G) is a monomorphism only if K(G) equals the centre Z(G) of G. The converse holds if K(G)=Z(G) is torsion free. We apply this criterion to many interesting classes of groups.

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