Theorems · Theorem · group theory
Subgroup.le_centralizer
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [h : IsMulCommutative ↥H], H ≤ Subgroup.centralizer ↑H- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- GroupIsMulCommutative
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 · 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 · cited by 65
- Subgroup.le_centralizer_iff_isMulCommutativeproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- Sylow.le_center_or_le_commutatorproof · cited by 1
- Sylow.conj_eq_normalizer_conj_of_memproof · cited by 1