Virtually splitting the map from 𝐴𝑢𝑡(𝐺) to 𝑂𝑢𝑡(𝐺)

Carette, Mathieu

doi:10.1090/S0002-9939-2014-12278-7

Virtually splitting the map from $\operatorname {Aut}(G)$ to $\operatorname {Out}(G)$
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Proc. Amer. Math. Soc. 143 (2015), 543-554 Request permission

Abstract:

We give an elementary criterion on a group $G$ for the map $\operatorname {Aut}(G)$ $\to \operatorname {Out}(G)$ to split virtually. This criterion applies to many residually finite $\operatorname {CAT}(0)$ groups and hyperbolic groups, and in particular to all finitely generated Coxeter groups. As a consequence the outer automorphism group of any finitely generated Coxeter group is residually finite and virtually torsion-free.

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