A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups

We give a short new proof that for each non-elementary Kleinian group $\Gamma$, the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of $\Gamma$, and that strict inequality holds if $\Gamma$ is of divergence type.