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We survey some properties of the automorphism groups of compact Kaehlermanifolds. In particular, we present recent results by Keum, Oguiso and Zhangon the structure of these groups from the Tits alternative point of view.Several other related results will be also discussed. This paper is written forthe VIASM Annual Meeting 2012.

Tits alternative for automorphism groups of compact Kaehler manifolds