Commensurations of Out(F n )
Publications Mathématiques de l'IHÉS, Volume 105  (2007), p. 1-48

Let Out(F n ) denote the outer automorphism group of the free group F n with n>3. We prove that for any finite index subgroup Γ<Out(F n ), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F n ). We prove that Γ is co-Hopfian: every injective homomorphism ΓΓ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F n )) is isomorphic to Out(F n ).

@article{PMIHES_2007__105__1_0,
     author = {Farb, Benson and Handel, Michael},
     title = {Commensurations of Out$(F\_n)$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {105},
     year = {2007},
     pages = {1-48},
     doi = {10.1007/s10240-007-0007-7},
     zbl = {pre05223500},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2007__105__1_0}
}
Farb, Benson; Handel, Michael. Commensurations of Out$(F_n)$. Publications Mathématiques de l'IHÉS, Volume 105 (2007) , pp. 1-48. doi : 10.1007/s10240-007-0007-7. http://www.numdam.org/item/PMIHES_2007__105__1_0/

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