Displaying similar documents to “Intersections of automorphism fixed subgroups in the free group of rank three.”

Commensurations of Out ( F n )

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).

The Automorphism Group of the Free Algebra of Rank Two

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...

On an algorithm to decide whether a free group is a free factor of another

Pedro V. Silva, Pascal Weil (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F . We show that the latter dependency can be made exponential in the rank difference rank ( F ) - rank ( H ) , which often makes a significant change.