  Let $A_{1} := k [t, \partial ]$ be the first algebra over a field $k$ of
characteristic zero. One can associate to each right ideal $I$ of $A_1$ its
Stafford subgroup, which is a subgroup of $\Aut_k(A_1)$, the automorphism group
of the ring $A_1$. In this article we show that each Stafford subgroup is equal
to its normalizer. For that, we study when the Stafford subgroup of a right
ideal of $A_1$ contains a given Stafford subgroup.
