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AutF2

Computations for the automorphisms group of F2

2.0

28 September 2026

Óscar Fernández Ayala
Email: oscar.fernandez-ayala@tu-braunschweig.de
Homepage: https://osferay.github.io/

Contents

2 Automorphisms

2.1 Automorphisms

  2.1-1 IsAutomorphismOfF2
  2.1-2 AutomorphismOfF2
  2.1-3 WordOfAutomorphismOfF2
  2.1-4 ImagesAutomorphismOfF2
  2.1-5 ImageByAutomorphismOfF2
  2.1-6 IsIdentityAutomorphismOfF2
  2.1-7 MatrixRepresentationOfAutomorphismOfF2
  2.1-8 IsSpecialAutomorphismOfF2
  2.1-9 IsConjugacyAutomorphismOfF2
  2.1-10 ConjugacyElementConjugacyAutomorphismOfF2
  2.1-11 ConjugacyAutomorphismOfF2
  2.1-12 AutomorphismOfF2ByImages
  2.1-13 AutomorphismOfF2ByMatrix

3 Conjugacy, fixed-point subgroups, and centralizers

3.1 Centralizer

3.1-1 CentralizerAutomorphismOfF2

3.2-1 AreConjugateAutomorphismsOfF2

3.3 Fixed points subgroup

3.3-1 FixedSubgroupAutomorphismOfF2

4 Related Algorithms

4.1 Matrix groups

  4.1-1 ConjugacyGL2Z
  4.1-2 CentralizerGL2Z
  4.1-3 MembershipSubgroupSL2Z

4.2 Free groups

  4.2-1 AreAutomorphicEquivalent
  4.2-2 IsCyclicalyReducedWord
  4.2-3 IsSubword
  4.2-4 IsPrefix
  4.2-5 IsSuffix
  4.2-6 RootFreeGroup
  4.2-7 NielsenReducedSet
  4.2-8 IsNielsenReducedSet
  4.2-9 InFreeSubgroup
  4.2-10 IsSubgroupOfFreeSubgroup
  4.2-11 IsNormalSubgroupOfFreeSubgroup
  4.2-12 AreEquivalent

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