For a positive integer $n$, with $n \geq 4$, let $R_{ n}$ be a free (nilpotent of class 2)-by-abelian and abelian-by-(nilpotent of class 2) Lie algebra of rank $n$. We show that the subgroup of Aut$(R_{ n})$ generated by the tame automorphisms and a countably infinite set of explicitly given automorphisms of $R_{ n}$ is dense in Aut$(R_{ n})$ with respect to the formal power series topology.
Categories: math.GR