Bien's conjecture on radical normal subgroups of division rings

Let $D$) be a division ring and let $K$ be a proper division subring of $D$. A subgroup is radical over $K$ if every one of its elements has a positive power in $K$.

Bien's conjecture. Every normal subgroup of $D^*$ that is radical over $K$ is commutative.

The conjecture generalizes Faith's theorem, which states that a division ring radical over a proper subring is commutative, from the full multiplicative group to normal subgroups. The source states that the conjecture remains open in general; it also notes that the analogous assertion can fail when $K$ is merely a subring rather than a division subring.