Structure
The abelianization map Fn → Zn induces a homomorphism Out(Fn) → GL(n, Z), the latter being the automorphism group of Zn. This map is onto, making Out(Fn) a group extension
- Tor(Fn) → Out(Fn) → GL(n, Z).
The kernel Tor(Fn) is the Torelli group of Fn.
In the case n = 2, the map Out(F2) → GL(2, Z) is an isomorphism.
Read more about this topic: Out(Fn)
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