# Margulis' normal subgroup theorem

Let $G$ be a connected, centerless semisimple Lie group of real rank at least 2. Let $\Gamma$ be an irreducible lattice in $G$. Then any nontrivial normal subgroup of $\Gamma$ has finite index. In other words, $G$ is a Group in which every nontrivial normal subgroup has finite index (?).