Theorems · Theorem · group theory
Subgroup.centralizer_eq_top_iff_subset
∀ {G : Type u_1} [inst : Group G] {s : Set G}, Subgroup.centralizer s = ⊤ ↔ s ⊆ ↑(Subgroup.center G)- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.centerstatement · cited by 121
- SetLike.ext'_iffproof · cited by 78
- Subgroup.centralizerstatement · cited by 65
- Set.centralizer_eq_top_iff_subsetproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Sylow.le_center_or_le_commutatorproof · cited by 1
- Subgroup.centralizer_centerproof · cited by 1