14.84 (1999)

An element $g$ of a (relatively) free group $F_r(\mathfrak{M})$ of rank $r$ of a variety $\mathfrak{M}$ is said to be primitive if it can be included in a basis of $F_r(\mathfrak{M})$.
$\qquad$ a) Do there exist a group $F_r(\mathfrak{M})$ and a non-primitive element $h \in F_r(\mathfrak{M})$ such that for some monomorphism $\alpha$ of $F_r(\mathfrak{M})$ the element $\alpha(h)$ is primitive?
$\qquad$ b) Do there exist a group $F_r(\mathfrak{M})$ and a non-primitive element $h \in F_r(\mathfrak{M})$ such that for some $n > r$ the element $h$ is primitive in $F_n(\mathfrak{M})$?