Theorems · Definition · group theory
MonoidHom.range
{G : Type u_1} → [inst : Group G] → {N : Type u_5} → [inst_1 : Group N] → (G →* N) → Subgroup NThe range of a monoid homomorphism from a group is a subgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 314 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 165 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Set.rangeproof · cited by 4,705
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Subgroup.mapproof · cited by 301
- Subgroup.copyproof · cited by 2
Cited by381
Results whose statement or proof uses this declaration.
- ClassGroupproof · cited by 50
- MonoidHom.range_eq_mapstatement · cited by 37
- MonoidHom.range_eq_topstatement · cited by 29
- Subgroup.range_subtypestatement and proof · cited by 28
- ClassGroup.mkproof · cited by 22
- MonoidHom.rangeRestrictstatement and proof · cited by 17
- MonoidHom.ofInjectivestatement and proof · cited by 12
- Matrix.det_fromBlocks_zero₂₁proof · cited by 10
- one_mem_strictPeriods_SLstatement · cited by 8
- CuspForm.discriminantEquivstatement and proof · cited by 8
- ClassGroup.extendedHomproof · cited by 7
- Subgroup.index_kerstatement and proof · cited by 7
Showing the 200 most cited of 381.