Theorems · Definition · group theory
Subgroup.centerUnitsEquivUnitsCenter
(G₀ : Type u_1) → [inst : GroupWithZero G₀] → ↥(Subgroup.center G₀ˣ) ≃* (↥(Submonoid.center G₀))ˣ
For a group with zero, the center of the units is the same as the units of the center.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- MulEquivstatement · cited by 1,142
- GroupWithZerostatement and proof · cited by 691
- Subgroup.centerstatement and proof · cited by 121
- Submonoid.centerstatement and proof · cited by 24
- MonoidHom.toHomUnitsproof · cited by 9
- unitsCenterToCenterUnitsproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.val_centerUnitsEquivUnitsCenter_apply_coestatement and proof · cited by 0
- Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coestatement and proof · cited by 0