An automorphism of a group $G$ is said to be normal if it stabilizes
each normal subgroup of $G$ setwise. We show that for any
non-elementary relatively hyperbolic group $G$, $Inn(G)$ has finite
index in the group of normal automorphisms $Aut_n(G)$ and
$Aut_n(G)=Inn(G)$ whenever $G$ contains no nontrivial finite normal
subgroups. Moreover, in the later case there exists a single normal
subgroup $N$ of $G$ such that every automorphism stabilizing $N$ is
inner. One of the main ingredients of the proof is group theoretic
Dehn surgery.

Lecture #12574

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