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Abstract. We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abeliani-zation. This implies that Aut(F3) does not have Kazhdan’s prop-erty (T) (see [3] and [6] for another proofs). We proved also that every subgroup of finite index in Aut(Fn), n> 3, which contains the subgroup of IA-automorphisms, has a finite abelianization. 1. Definitions, problems and motivations The Kazhdan property (T) was introduced by D. Kazhdan in 1967 in his investigations on Lie groups. Let H be a Hilbert space and U(H) be the group of unitary transforma-tions of H. Definition 1.1. A discrete group G has Kazhdan’s property (T) if there exists an ε> 0 and a finite subset S ⊂ G such that for all nontrivial irreducible representations ρ: G → U(H) and for all vectors v ∈ H with ||v| | = 1 we have ||ρ(s)v − v| |> ε for some s ∈ S. It is known, that in this case S generates G. Definition 1.2. A group G has Serre’s property (FA) if acting simplicially and without inversions of edges on any simplicial tree, G has a global fixed point. Theorem 1.3. (J.-P. Serre; 1974). A finitely generated group G has the property (FA) if and only if the following two statements hold: (1) G is not a nontrivial amalgamated product, that is G A ∗B C with B 6 = A and B 6 = C, (2) G does not have a quotient which is isomorphic to Z, This paper was prepared while the first-named author was a visitor at Centre d