Appears in collection : 2022 - T2 - WS1 - Mapping class groups and Out(Fn)

This is joint work with Stephane Lamy. Let $k$ be a field of characteristic zero. The tame automorphism group Tame$(k^3)$ is generated by the affine automorphisms of $k^3$, and the automorphisms of the form $(x,y,z) → (x,y,z + P(x,y))$, where P is a polynomial in $k[x,y]$. We prove that every subgroup of Tame$(k^3)$ is virtually solvable or contains a nonabelian free group.