4.34 (1973)

Let $v$ be a group word, and let $\mathfrak{K}_v$ be the class of groups $G$ such that there exists a positive integer $n = n(G)$ such that each element of the verbal subgroup $vG$ can be represented as a product of $n$ values of the word $v$ on the group $G$.
$\qquad$ a) For which $v$ do all finitely generated soluble groups belong to the class $\mathfrak{K}_v$?
$\qquad$ b) Does the word $v(x, y) = x^{-1}y^{-1}xy$ satisfy this condition?