Algebraic sets in metabelian groups

The research launched in [Algebra i Logika, 44, № 5 (2005), 601–621] is brought to a close by examining algebraic sets in a metabelian group $G$ in two important cases: (1) $G=F_n$ is a free metabelian group of rank $n$; (2) $G=W_{n,k}$ is a wreath product of free Abelian groups of ranks $n$ and $k$.