Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 4 / 4 / i / Solution

The first Baumslag-Solitar group iswhere the second infinite cyclic group acts on the first by inversion. The presentation of a semidirect product proves this identification; both copies of $\mathbb{Z}$ are residually finite groups, since reduction modulo a suitable positive integer separates any nonzero integer. The normal factor is finitely generated, so the residual finiteness of semidirect products theorem applies. $\boxed{BS(1,-1)\text{ is residually finite}.}$