  We develop a method for analyzing the mixing times for a quite general class
of Markov chains on the complete monomial group G \wr S_n (the wreath product
of a group G with the permutation group S_n) and a quite general class of
Markov chains on the homogeneous space (G \wr S_n) / (S_r \times S_{n - r}).
  We derive an exact formula for the L^2 distance in terms of the L^2 distances
to uniformity for closely related random walks on the symmetric groups S_j for
1 \leq j \leq n or for closely related Markov chains on the homogeneous spaces
S_{i + j} / (S_i \times S_j) for various values of i and j, respectively. Our
results are consistent with those previously known, but our method is
considerably simpler and more general.
