On the profinite topology of the automorphism group of a residually torsion free nilpotent group (Q1293414)

The profinite topology on a group \(G\) is the topology in which a base of the open sets is the set of all cosets of normal subgroups of finite index in \(G\). The authors prove that if \(G\) is a finitely generated residually torsion-free nilpotent group, then every polycyclic-by-finite subgroup of \(\Aut G\), the automorphism group or \(G\), is closed in the profinite topology on \(\Aut G\). This result implies, in particular, that if \(G\) is either free of finite rank or a surface group, then every polycyclic-by-finite subgroup of \(\Aut G\) is closed in the profinite topology on \(\Aut G\).