Theorems · Theorem · group theory
commutator_def
∀ (G : Type u_1) [inst : Group G], commutator G = ⁅⊤, ⊤⁆
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Bracket.bracketstatement · cited by 642
- commutatorstatement · cited by 56
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.map_subtype_commutatorproof · cited by 7
- Group.IsPerfect.top_iffproof · cited by 1
- IsZGroup.isCyclic_commutatorproof · cited by 1
- Sylow.le_center_or_le_commutatorproof · cited by 1
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- map_commutator_eqproof · cited by 0