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## Infinite transitivity and special automorphisms

It is known that if the special automorphism group SAut(X) of a quasiaffine variety X of dimension at least 2 acts transitively on X, then this action is infinitely transitive. In this paper we address the question whether this is the only possibility for the automorphism group Aut(X) to act infinitely transitively on X. We show that this is the case provided X admits a nontrivial G_a or G_m-action. Moreover, 2-transitivity of the automorphism group implies infinite transitivity.