  In this paper, it is shown that every point in the hyperbolic 3-space is
moved at a distance at least $0.5\log\left(12\cdot 3^{k-1}-3\right)$ by one of
the isometries of length at most $k\geq 2$ in a 2-generator Klenian group
$\Gamma$ which is torsion-free, not co-compact and contains no parabolic. Also
some lower bounds for the maximum of hyperbolic displacements given by
symmetric subsets of isometries in purely loxodromic finitely generated free
Kleinian groups are conjectured.
