Theorems · Definition · group theory
Subgroup.quotConjEquiv
{G : Type u_1} →
[inst : Group G] → (H K : Subgroup G) → (g : ConjAct G) → ↥K ⧸ H.subgroupOf K ≃ ↥(g • K) ⧸ (g • H).subgroupOf (g • K)Equivalence of K / (H ⊓ K) with gKg⁻¹/ (gHg⁻¹ ⊓ gKg⁻¹)
- Defined in
- Mathlib.GroupTheory.Commensurable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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 · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- MulEquiv.toEquivproof · cited by 126
- Subgroup.subgroupOfstatement · cited by 122
- ConjActstatement and proof · cited by 79
- Subgroup.pointwiseMulActionstatement · cited by 66
- Subgroup.equivSMulproof · cited by 2
- Quotient.congrproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.Commensurable.commensurable_conjproof · cited by 3