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Indicability of $\mathrm{Out}(F_n)$
A group $G$ is said to be indicable if it surjects onto $\mathbb{Z}$.
If $n=1$: $\mathrm{Out}(F_1)=\mathbb{Z}/2\mathbb{Z}$ and no finite group surjects onto an infinite group.
If $n\geq 4$: $\...
- 911
7
votes
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$\operatorname{Out}(F_n)$ is not linear for $n > 3$
The paper The Tits alternative for $\operatorname{Out}(F_n)$ I by Bestvina, Feighn and Handel and the paper Automorphisms of free groups and Outer space by Vogtmann both state that $\operatorname{Aut}(...
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