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We study the outer automorphism group OutRr of the ergodic equivalence relation Rr generated by the action of a lattice F in a semisimple Lie group on the homogeneos space of a compact group K. It is shown that OutRr is locally compact. If K is a connected simple Lie group, we prove the compactness of 0\itRr using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.

Outer automorphism group of the ergodic equivalence relation generated by translations of dense subgroup of compact group on its homogeneous space