  We study the L^p-distortion of finite quotients of amenable groups. In
particular, for every number p larger or equal than 2, we prove that the
l^p-distortion of the finite lamplighter group grows like (\log n)^{1/p}. We
also give the asymptotic behavior of the l^p-distortion of finite quotients of
certain metabelian polycyclic groups and of the solvable Baumslag-Solitar
groups BS(m,1). The proofs are short and elementary.
