Theorems · Theorem · group theory
MonoidHom.mem_ker
∀ {G : Type u_1} [inst : Group G] {M : Type u_7} [inst_1 : MulOneClass M] {f : G →* M} {x : G}, x ∈ f.ker ↔ f x = 1- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- GroupMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.kerstatement · cited by 212
Cited by22
Results whose statement or proof uses this declaration.
- Equiv.Perm.mem_alternatingGroupproof · cited by 7
- DirichletCharacter.factorsThrough_iff_ker_unitsMapproof · cited by 4
- QuotientGroup.kerLift_injectiveproof · cited by 3
- MonoidHom.eq_iffproof · cited by 2
- IsMulTorsion.extension_closedproof · cited by 2
- MonoidHom.liftOfRightInverseAux_comp_applyproof · cited by 1
- TopologicalGroup.IsSES.integral_pullback_invFun_applyproof · cited by 1
- DirichletCharacter.factorsThrough_gcdproof · cited by 1
- FixedPoints.toAlgAut_surjectiveproof · cited by 1
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfproof · cited by 1
- PresentedGroup.closure_rels_subset_kerproof · cited by 1
- GroupExtension.rightHom_inlproof · cited by 1