Margulis' normal subgroup theorem
This is an example of a normal subgroup theorem, viz a result that states that under certain circumstances, every nontrivial normal subgroup must be of finite index
Let be a connected, centerless semisimple Lie group of real rank at least 2. Let be an irreducible lattice in . Then any nontrivial normal subgroup of has finite index. In other words, is a Group in which every nontrivial normal subgroup has finite index (?).