When are centralizers of finite subgroups of Out(Fn) finite?
نویسندگان
چکیده
This paper gives necessary and sufficient conditions for the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) of a finitely generated free group to be finite. If G is realized by its action on a graph, Krstić’s work produces generators of the centralizer of G in terms of graph isomorphisms and certain graph transformations. This paper examines the behavior of these graph transformations to determine criteria for a centralizer to be finite. This result extends that of Krstić and Vogtmann on finite centralizers. It also gives alternate criteria to that provided by Pettet for a free-by-finite group to have a finite outer automorphism group.
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