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We show that any compact group can be realized as the outer automorphismgroup of a factor of type II_1. This has been proved in the abelian case byIoana, Peterson and Popa applying Popa's deformation/rigidity techniques toamalgamated free product von Neumann algebras. Our methods are a generalizationof theirs.

Every compact group arises as the outer automorphism group of a II_1 factor