Theorems · Definition · group theory
Subgroup.centralizer
{G : Type u_1} → [inst : Group G] → Set G → Subgroup GThe centralizer of s is the subgroup of g : G commuting with every h : s.
- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 14 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.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Submonoidproof · cited by 3,086
- Submonoid.centralizerproof · cited by 15
- Set.inv_mem_centralizerproof · cited by 1
Cited by71
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.toPermHomstatement and proof · cited by 12
- MonoidHom.transferSylowstatement and proof · cited by 9
- Equiv.Perm.Basis.toCentralizerstatement · cited by 5
- Subgroup.commutator_eq_bot_iff_le_centralizerstatement and proof · cited by 5
- Subgroup.mem_centralizer_singleton_iffstatement · cited by 4
- Subgroup.centralizer_eq_top_iff_subsetstatement · cited by 3
- Subgroup.centralizer_univstatement · cited by 3
- MonoidHom.ker_transferSylow_isComplement'statement and proof · cited by 3
- Subgroup.le_centralizerstatement · cited by 3
- Subgroup.le_centralizer_iffstatement and proof · cited by 3
- Equiv.Perm.OnCycleFactors.kerParam_range_eqstatement and proof · cited by 3
- Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iffstatement and proof · cited by 3