  We show that if $\pi$ is the fundamental group of a 4-dimensional
infrasolvmanifold then $-2\leq{def(\pi)}\leq0$, and give examples realizing
each of these values. We also determine the abstract commensurators of such
groups. Finally we show that if $G$ is a finitely generated group the kernel of
the natural homomorphism from $G$ to its abstract commensurator $Comm(G)$ is
locally nilpotent by locally finite, and is finite if $\mathrm{def}(G)>1$.
