Intersections of automorphism fixed subgroups in the free group of rank three.
Martino, A. (2004)
Algebraic & Geometric Topology
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Martino, A. (2004)
Algebraic & Geometric Topology
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Crisp, John (2005)
Geometry & Topology
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Feighn, Mark, Handel, Michael (1999)
Annals of Mathematics. Second Series
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Benson Farb, Michael Handel (2007)
Publications Mathématiques de l'IHÉS
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Let Out(F) denote the outer automorphism group of the free group F with >3. We prove that for any finite index subgroup Γ<Out(F), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F). We prove that Γ is : every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F)) is isomorphic to Out(F).
Jensen, Craig A., Wahl, Nathalie (2004)
Algebraic & Geometric Topology
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Fried, Stephanie, Gerek, Aydin, Gordon, Gary, Perunicic, Andrija (2007)
The Electronic Journal of Combinatorics [electronic only]
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Haralick, R.M., Miasnikov, A.D., Myasnikov, A.G. (2005)
Experimental Mathematics
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Gutierrez, Mauricio, Kaul, Anton (2008)
International Journal of Mathematics and Mathematical Sciences
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Franzsen, W.N., Howlett, R.B. (2003)
Advances in Geometry
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Cohn, P. (2002)
Serdica Mathematical Journal
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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate...