Theorems · Definition · group theory

Equiv.altCongrHom

{α : Type u_1} →
  [inst : Fintype α] →
    [inst_1 : DecidableEq α] →
      {β : Type u_2} →
        [inst_2 : Fintype β] → [inst_3 : DecidableEq β] → α ≃ β → ↥(alternatingGroup α) ≃* ↥(alternatingGroup β)

The group isomorphism between alternatingGroups induced by the given Equiv.

Defined in: Mathlib.GroupTheory.SpecificGroups.Alternating
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableEq Fintype DecidableEq

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Around this declaration

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

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Equivstatement and proof · cited by 8,337
Fintypestatement and proof · cited by 7,736
Subgroupstatement · cited by 3,593
Equiv.Permstatement · cited by 1,375
MulEquivstatement · cited by 1,142
alternatingGroupstatement and proof · cited by 96
MulEquiv.transproof · cited by 53
MulEquiv.subgroupCongrproof · cited by 10
MulEquiv.subgroupMapproof · cited by 4
Equiv.permCongrHomproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

Equiv.altCongrHom_apply_coestatement and proof · cited by 0