  While lattices in semi-simple Lie groups are studied very well, only little
is known about discrete subgroups of infinite covolume. The main class of
examples are Schottky groups. Here we investigate some new examples.
  We consider subgroups $\Gamma$ of arithmetic groups in $PSL(2,C)^q \times
PSL(2,R)^r$ with $q+r>1$ and their limit set. We prove that the projective
limit set of a nonelementary finitely generated $\Gamma$ consists of exactly
one point if and only if one and hence all projections of $\Gamma$ to the
simple factors of $PSL(2,C)^q \times PSL(2,R)^r$ are subgroups of arithmetic
Fuchsian or Kleinian groups. Furthermore, we study the topology of the whole
limit set of $\Gamma$. In particular, we give a necessary and sufficient
condition for the limit set to be homeomorphic to a circle.
