In the thesis of the second author it was shown for a suitable power $n$ of a
pair of Pell units $u,v$ of the quaternions algebras over the ring of integers
of imaginary rational extensions $\A=\h(\oo_{\Q \sqrt{-d}})$ that the group
generated by $u^ n,v^n$ is a free group in the unit group of $\A$ when $d
\equiv 7 \pmod 8$ is a positive square free integer. We extend this result and,
as an application of the Pell units, we construct free groups in the
quaternions algebras over the ring of integers of imaginary rational
extensions, using the Ping-Pong Lemma. Also we prove a criterium to a pair of
elements generate a free semigroup, with no use of the Ping-Pong Lemma.