This is false for torsion free uniform lattices in rank one semi simple Lie groups and large n $n$ by a result of Ivanov and Olshanskii, which implies that the normal subgroup generated by nth $n$th powers is infinite index for certain large n. $n$.
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This is false for torsion free uniform lattices in rank one semi simple Lie groups and large n by a result of Olshanskii, which implies that the normal subgroup generated by nth powers is infinite index for large n. |
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