Sieve methods in group theory \Rmnum{3}: $\aut(F_n)$

Let $π:\aut(F_n)\rightarrow \aut(\Z^n)$ be the epimorphism induced by the isomorphism $\Z^n \cong F_n/F_n'$ and define $\mathcal{T}_n:=\kerπ$. We prove that the subset of $\mathcal{T}_n$ consists of all non-iwip and all non-hyperbolic elements is exponentially small.

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