# Margulis' normal subgroup theorem

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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

## Statement

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 (?).