Theorems · Theorem · group theory
Subgroup.map_subtype_commutator
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), Subgroup.map H.subtype (commutator ↥H) = ⁅H, H⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.mapstatement and proof · cited by 301
- Subgroup.subtypestatement and proof · cited by 185
- commutatorstatement · cited by 56
- MonoidHom.range_eq_mapproof · cited by 37
- Subgroup.range_subtypeproof · cited by 28
- Subgroup.map_commutatorproof · cited by 12
- commutator_defproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.isPerfect_iffproof · cited by 2
- commutator_alternatingGroup_eq_selfproof · cited by 1
- Subgroup.commutator_le_selfproof · cited by 1
- IsZGroup.isCyclic_commutatorproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Group.IsPerfect.top_iffproof · cited by 1
- Subgroup.commutator_le_focalSubgroupproof · cited by 0