Theorems · Theorem · group theory
Set.inv_mem_centralizer
∀ {M : Type u_1} {S : Set M} [inst : Group M] {a : M}, a ∈ S.centralizer → a⁻¹ ∈ S.centralizer- Defined in
- Mathlib.Algebra.Group.Center
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- 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
- mul_assocproof · cited by 1,667
- Set.centralizerstatement and proof · cited by 57
- mul_inv_eq_iff_eq_mulproof · cited by 13
- eq_inv_mul_iff_mul_eqproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.centralizerproof · cited by 65
- Set.div_mem_centralizerproof · cited by 0