Ascending HNN extensions of polycyclic groups are residually finite

AbstractWe prove that every ascending HNN extension of a polycyclic-by-finite group is residually finite. We also give a criterion for the residual finiteness of an ascending HNN extension of a residually nilpotent group, and apply this criterion to recover a result of Moldavanskiı̆ on the residual finiteness of certain ascending HNN extensions of free groups