Theorems · Definition · group theory
Submonoid.center
(M : Type u_1) → [inst : MulOneClass M] → Submonoid M
The center of a multiplication with unit M is the set of elements that commute with everything
in M
- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulOneClass
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.
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Set.centerproof · cited by 49
- Set.one_mem_centerproof · cited by 0
Cited by34
Results whose statement or proof uses this declaration.
- Subgroup.centerproof · cited by 121
- Representation.IntertwiningMap.centralAlgebraMulstatement and proof · cited by 3
- Subgroup.centerUnitsEquivUnitsCenterstatement and proof · cited by 2
- unitsCenterToCenterUnitsstatement and proof · cited by 2
- Submonoid.centerCongrstatement · cited by 2
- Submonoid.centerToMulOppositestatement · cited by 2
- Representation.IntertwiningMap.centralAlgebraMulHomstatement and proof · cited by 1
- Submonoid.mem_center_iffstatement and proof · cited by 1
- Representation.IntertwiningMap.centralAlgebraMulHom_applystatement and proof · cited by 0
- Representation.IntertwiningMap.centralAlgebraMul_applystatement and proof · cited by 0
- Representation.IntertwiningMap.centralMulstatement and proof · cited by 0
- Module.End.mem_submonoidCenter_iffstatement · cited by 0