We prove in a large number of cases, that a Zariski dense discrete subgroup of a simple real algebraic group $G$ which contains a higher rank lattice is a lattice in the group $G$. For example, we show that a Zariski dense subgroup of $SL_n({ \mathbb R})$ which contains $SL_3({ \mathbb Z})$ in the top left hand corner, is conjugate to $SL_n({ \mathbb Z})$ .
Categories: math.GR