STRONGLY JORDAN PROPERTY AND FREE ACTIONS OF NON-ABELIAN FREE GROUPS

Let X be a connected complex manifold and let. Z be a compact. complex subspace of X. Assume that Aut(Z) is strongly Jordan. In this paper, we show that the automorphism group Aut(X, Z) of all biholomorphisms of X preserving Z is strongly Jordan. A similar result has been proved by Meng et al. for a compact Ktiller submanifold Z of X instead of a compact complex subspace Z of X. In addition, we also show some rigidity result for free actions of large groups on complex manifolds.