Theorems · Theorem · group theory
Subgroup.closure_le_centralizer_centralizer
∀ {G : Type u_1} [inst : Group G] (s : Set G), Subgroup.closure s ≤ Subgroup.centralizer ↑(Subgroup.centralizer s)- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites8
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.closurestatement · cited by 196
- Subgroup.centralizerstatement and proof · cited by 65
- Subgroup.closure_leproof · cited by 31
- Set.subset_centralizer_centralizerproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.centralizer_closureproof · cited by 1
- Subgroup.isMulCommutative_closureproof · cited by 0