  Given a field $k$ and a finite group $G$, the Beckmann--Black problem asks
whether every Galois field extension $F/k$ with group $G$ is the specialization
at some $t_0 \in k$ of some Galois field extension $E/k(T)$ with group $G$ and
$E \cap \overline{k} = k$. We show that the answer is positive for arbitrary
$k$ and $G$, if one waives the requirement that $E/k(T)$ is normal. In fact,
our result holds if ${\rm{Gal}}(F/k)$ is any given subgroup $H$ of $G$ and, in
the special case $H=G$, we provide a similar conclusion even if $F/k$ is not
normal. We next derive that, given a division ring $H$ and an automorphism
$\sigma$ of $H$ of finite order, all finite groups occur as automorphism groups
over the skew field of fractions $H(T, \sigma)$ of the twisted polynomial ring
$H[T, \sigma]$.
