Theorems · Definition · group theory

Subgroup.equivSMul

{α : Type u_1} →
  {G : Type u_2} →
    [inst : Group G] →
      [inst_1 : Group α] → [inst_2 : MulDistribMulAction α G] → (a : α) → (H : Subgroup G) → ↥H ≃* ↥(a • H)

Applying a MulDistribMulAction results in an isomorphic subgroup

Defined in: Mathlib.Algebra.Group.Subgroup.Pointwise
Cited by: 2 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group Group MulDistribMulAction

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Cites7

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

Groupstatement and proof · cited by 6,238
Subgroupstatement and proof · cited by 3,593
MulEquivstatement · cited by 1,142
MulDistribMulActionstatement and proof · cited by 120
Subgroup.pointwiseMulActionstatement · cited by 66
MulDistribMulAction.toMulEquivproof · cited by 5
MulEquiv.subgroupMapproof · cited by 4

Cited by4

Results whose statement or proof uses this declaration.

Subgroup.quotConjEquivproof · cited by 1
Sylow.equivSMulproof · cited by 0
Subgroup.equivSMul_apply_coestatement and proof · cited by 0
Subgroup.equivSMul_symm_apply_coestatement and proof · cited by 0