  In recent years, knapsack problems for (in general non-commutative) groups
have attracted attention. In this paper, the knapsack problem for wreath
products is studied. It turns out that decidability of knapsack is not
preserved under wreath product. On the other hand, the class of
knapsack-semilinear groups, where solutions sets of knapsack equations are
effectively semilinear, is closed under wreath product. As a consequence, we
obtain the decidability of knapsack for free solvable groups. Finally, it is
shown that for every non-trivial abelian group $G$, knapsack (as well as the
related subset sum problem) for the wreath product $G \wr \mathbb{Z}$ is
NP-complete.
