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AutF2

Computations for the automorphisms group of F2

1.0

17 March 2026

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

Contents

1 Automorphisms

1.1 Automorphisms

  1.1-1 IsAutomorphismOfF2
  1.1-2 AutomorphismOfF2
  1.1-3 WordOfAutomorphismOfF2
  1.1-4 ImagesAutomorphismOfF2
  1.1-5 ImageByAutomorphismOfF2
  1.1-6 IsIdentityAutomorphismOfF2
  1.1-7 MatrixRepresentationOfAutomorphismOfF2
  1.1-8 IsSpecialAutomorphismOfF2
  1.1-9 IsConjugacyAutomorphismOfF2
  1.1-10 ConjugacyElementConjugacyAutomorphismOfF2
  1.1-11 ConjugacyAutomorphismOfF2

1.2 Recognizing automorphisms

1.2-1 AutomorphismOfF2ByImages
1.2-2 AutomorphismOfF2ByMatrix

2 Conjugacy, fixed points subgroup and centralizer

2.1 Centralizer

2.1-1 CentralizerAutomorphismOfF2

2.2-1 AreConjugateAutomorphismsOfF2

2.3 Fixed points subgroup

2.3-1 FixedSubgroupAutomorphismOfF2

3 Related Algorithms

3.1 Matrix groups

  3.1-1 ConjugacyGL2Z
  3.1-2 CentralizerGL2Z
  3.1-3 MembershipSubgroupSL2Z

3.2 Free groups

  3.2-1 AreAutomorphicEquivalent
  3.2-2 IsCyclicalyReducedWord
  3.2-3 IsSubword
  3.2-4 IsPrefix
  3.2-5 IsSuffix
  3.2-6 RootFreeGroup
  3.2-7 NielsenReducedSet
  3.2-8 IsNielsenReducedSet
  3.2-9 InFreeSubgroup
  3.2-10 IsSubgroupOfFreeSubgroup
  3.2-11 IsNormalSubgroupOfFreeSubgroup
  3.2-12 AreEquivalent

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