  We bound the rate of convergence to uniformity for certain random walks on
the complete monomial groups G \wr S_n for any group G. These results provide
rates of convergence for random walks on a number of groups of interest: the
hyperoctahedral group Z_2 \wr S_n, the generalized symmetric group Z_m \wr S_n,
and S_m \wr S_n. These results provide benchmarks to which many other random
walks, modeling a wide range of phenomena, may be compared using the comparison
technique, thereby yielding bounds on the rates of convergence to uniformity
for previously intractable random walks.
