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We show that the group factors of ICC lattices in either SO(n,1) or SU(n,1),n \geq 2, are strongly solid in the sense of Ozawa and Popa. This strengthens aresult of Ozawa and Popa showing that these factors do not have Cartansubalgebras.

Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)