Theorems · Definition · group theory
commutatorSet
(G : Type u_1) → [Group G] → Set G
The set of commutator elements ⁅g₁, g₂⁆ in G.
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Bracket.bracketproof · cited by 642
Cited by23
Results whose statement or proof uses this declaration.
- commutator_eq_closurestatement · cited by 7
- Abelianization.commutator_subset_kerproof · cited by 5
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- image_commutatorSet_closureCommutatorRepresentativesstatement and proof · cited by 2
- Subgroup.quotientCenterEmbeddingstatement · cited by 2
- Subgroup.rank_commutator_le_cardstatement and proof · cited by 1
- commutatorRepresentativesproof · cited by 1
- Subgroup.index_center_le_powstatement and proof · cited by 1
- Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroupstatement · cited by 1
- commutator_eq_normalClosurestatement · cited by 1
- commutator_mem_commutatorSetstatement · cited by 1
- Subgroup.card_commutator_dvd_index_center_powstatement and proof · cited by 1