# Homomorphisms from automorphism groups of free groups

@inproceedings{Vogtmann2002HomomorphismsFA,
title={Homomorphisms from automorphism groups of free groups},
author={Martin R BridsonKaren Vogtmann},
year={2002}
}
The automorphism group of a finitely generated free group is the normal closure of a single element of order 2. If $m$ is less than $n$ then a homomorphism $Aut(F_n)\to Aut(F_m)$ can have cardinality at most 2. More generally, this is true of homomorphisms from $\Aut(F_n)$ to any group that does not contain an isomorphic copy of the symmetric group $S_{n+1}$. Strong constraints are also obtained on maps to groups that do not contain a copy of $W_n= (\Bbb Z/2)^n\rtimes S_n$, or of \$\Bbb Z^{n-1… CONTINUE READING
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