Theorems · Definition · group theory
MulEquiv.subgroupCongr
{G : Type u_1} → [inst : Group G] → {H K : Subgroup G} → H = K → ↥H ≃* ↥KMakes the identity isomorphism from a proof two subgroups of a multiplicative group are equal.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement · cited by 1,142
- Equiv.setCongrproof · cited by 13
Cited by20
Results whose statement or proof uses this declaration.
- MulAction.stabilizerEquivStabilizerproof · cited by 16
- SubMulAction.fixingSubgroupEquivFixingSubgroupproof · cited by 5
- autEquivZmodproof · cited by 5
- rootsOfUnityEquivOfPrimitiveRootsproof · cited by 5
- SubMulAction.ofFixingSubgroup_of_eqstatement · cited by 2
- ClassGroup.equivPicproof · cited by 2
- Submodule.unitsQuotEquivRelPicproof · cited by 2
- Subgroup.exponent_toSubmonoidproof · cited by 1
- SubMulAction.ofFixingSubgroup_of_eq_bijectivestatement · cited by 1
- autEquivZmod_symm_apply_intCastproof · cited by 1
- Equiv.altCongrHomproof · cited by 1
- Int.subgroup_index_ne_zero_iffproof · cited by 0