Theorems · Theorem · group theory
Subgroup.mem_centralizer_singleton_iff
∀ {G : Type u_1} [inst : Group G] {g k : G}, k ∈ Subgroup.centralizer {g} ↔ k * g = g * k- Defined in
- Mathlib.GroupTheory.Subgroup.Centralizer
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.centralizerstatement · cited by 65
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.kerParam_range_eqproof · cited by 3
- Equiv.Perm.OnCycleFactors.odd_of_centralizer_le_alternatingGroupproof · cited by 2
- Equiv.Perm.Basis.ofPermHom_mem_centralizerproof · cited by 0