Theorems · Theorem · group theory
MonoidHom.finite_iff_finite_ker_range
∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] (f : G →* G'),
Finite G ↔ Finite ↥f.ker ∧ Finite ↥f.range- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientproof · cited by 2,301
- MonoidHom.rangestatement and proof · cited by 314
- MonoidHom.kerstatement and proof · cited by 212
- MulEquiv.toEquivproof · cited by 126
- Subgroup.FiniteIndexproof · cited by 113
- Equiv.finite_iffproof · cited by 21
- QuotientGroup.quotientKerEquivRangeproof · cited by 7
- Subgroup.finiteIndex_iff_finite_quotientproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1