Theorems · Definition · group theory
Subgroup.ofUnits
{M : Type u_1} → [inst : Monoid M] → Subgroup Mˣ → Submonoid MA subgroup of units represented as a submonoid of M.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Subgroupstatement and proof · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Submonoid.mapproof · cited by 190
- Subgroup.toSubmonoidproof · cited by 114
- Units.coeHomproof · cited by 44
Cited by35
Results whose statement or proof uses this declaration.
- ofUnits_units_gcstatement · cited by 11
- ofUnits_units_gcistatement · cited by 10
- Subgroup.unit_of_mem_ofUnitsstatement and proof · cited by 4
- Subgroup.unit_eq_unit_of_mem_ofUnitsstatement and proof · cited by 1
- Subgroup.unit_mem_of_mem_ofUnitsstatement and proof · cited by 1
- Subgroup.unit_of_mem_ofUnits_spec_memstatement and proof · cited by 1
- Subgroup.isUnit_of_mem_ofUnitsstatement and proof · cited by 1
- Subgroup.mem_ofUnitsstatement · cited by 1
- Subgroup.mem_ofUnits_of_isUnit_of_unit_memstatement · cited by 1
- Subgroup.mem_of_mem_val_ofUnitsstatement and proof · cited by 1
- Subgroup.ofUnitsEquivTypestatement and proof · cited by 0
- Subgroup.ofUnitsTopEquivstatement · cited by 0