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 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 (?).

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