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For a coefficient free cluster algebra A, we study the cluster automorphism group Aut(A) and the automorphism group Aut(E_A) of its exchange graph E_A. We show that these two groups are isomorphic with each other, if A is of finite type excepting types of rank two and type F_4, or if A is of skew-symmetric finite mutation type.arXiv:1506.02029v3 fatcat:2ougwxrpbng47e4khegff4y6ua