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Theorems · Definition · group theory

PresentedGroup.equivPresentedGroup

{α : Type u_1} →
  {β : Type u_2} →
    (rels : Set (FreeGroup α)) →
      (e : α ≃ β) → PresentedGroup rels ≃* PresentedGroup (⇑(FreeGroup.freeGroupCongr e) '' rels)

Presented groups of isomorphic types are isomorphic.

Defined in
Mathlib.GroupTheory.PresentedGroup
Cited by
2 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PresentedGroup.equivPresentedGroup_apply_of · cited by 0PresentedGroup.equivPrese…PresentedGroup.equivPresentedGroup_symm_apply_of · cited by 0PresentedGroup.equivPrese…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetEquiv · cited by 8337EquivSet.image · cited by 5609Set.imageMulEquiv · cited by 1142MulEquivFreeGroup · cited by 132FreeGroupSubgroup.normalClosure · cited by 35Subgroup.normalClosurePresentedGroup · cited by 21PresentedGroupQuotientGroup.congr · cited by 16QuotientGroup.congrFreeGroup.freeGroupCongr · cited by 8FreeGroup.freeGroupCongrPresentedGroup.equivPresented…CITED BYCITES

Cites10

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Cited by2

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