  The classic Magnus embedding is a very effective tool in the study of abelian
extensions of a finitely generated group $G$, allowing us to see the extension
as a subgroup of a wreath product of a free abelian group with $G$. In
particular, the embedding has proved to be useful when studying free solvable
groups. An equivalent geometric definition of the Magnus embedding is
constructed and it is used to show that it is 2-bi-Lipschitz, with respect to
an obvious choice of generating sets. This is then applied to obtain a non-zero
lower bound on $L_p$ compression exponents in free solvable groups.
