Theorems · Theorem · group theory
Submonoid.mem_center_iff
∀ {M : Type u_1} [inst : Monoid M] {z : M}, z ∈ Submonoid.center M ↔ ∀ (g : M), g * z = z * g- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Submonoid.centerstatement and proof · cited by 24
- Semigroup.mem_center_iffproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Representation.IntertwiningMap.isIntertwiningMap_of_mem_centerproof · cited by 0