Log-space complexity of the conjugacy problem in wreath products

We show a transfer result from individual groups to wreath products. Namely, we prove that the conjugacy problem in the wreath product AB of two groups A and B is log-space decidable, provided the factor groups A and B both have log-space decidable conjugacy problem and B has log-space computable power problem. If, additionally, A and B have bounded torsion and A has log-space computable power problem, we show that the iterated wreath product AnB also has log-space decidable conjugacy problem. We apply these general results to show that free solvable groups and wreath products of two abelian groups (in particular, the lamplighter group, Z2 = Z) have log-space decidable conjugacy problem.