Margulis' normal subgroup theorem

Statement
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 fact about::group in which every nontrivial normal subgroup has finite index.

Related facts

 * Burger-Mozes normal subgroup theorem