  Wreath products such as Z wr Z are not finitely-presentable yet can occur as
subgroups of finitely presented groups. Here we compute the distortion of Z wr
Z as a subgroup of Thompson's group F and as a subgroup of Baumslag's
metabelian group G.
  We find that Z wr Z is undistorted in F but is at least exponentially
distorted in G.
