  Let $D$ be a division ring with center $F$ and $N$ a subnormal subgroup of
the multiplicative group $D^*$ of $D$. Assume that $N$ contains a non-abelian
solvable subgroup. In this paper, we study the problem on the existence of
non-abelian free subgroups in $N$. In particular, we show that if either $N$ is
algebraic over $F$ or $F$ is uncountable, then $N$ contains a non-abelian free
subgroup.
