Theorems · Theorem · group theory
Subgroup.le_centralizer_iff_isMulCommutative
∀ {G : Type u_1} [inst : Group G] {K : Subgroup G}, K ≤ Subgroup.centralizer ↑K ↔ IsMulCommutative ↥K- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- IsMulCommutativestatement and proof · cited by 95
- Subgroup.centralizerstatement and proof · cited by 65
- mul_comm'proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.le_centralizerproof · cited by 3
- Subgroup.commutator_self_eq_bot_iffproof · cited by 0