Theorems · Theorem · group theory
Group.isCyclic_of_coprime_card_range_card_ker
∀ {M : Type u_4} {N : Type u_5} [inst : CommGroup M] [inst_1 : Group N] (f : M →* N),
(Nat.card ↥f.ker).Coprime (Nat.card ↥f.range) → ∀ [IsCyclic ↥f.ker] [IsCyclic ↥f.range], IsCyclic M- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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 and proof · cited by 3,593
- Finiteproof · cited by 3,029
- CommGroupstatement and proof · cited by 990
- Nat.cardstatement and proof · cited by 844
- Infiniteproof · cited by 352
- MonoidHom.rangestatement and proof · cited by 314
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.subtypeproof · cited by 185
- Monoid.exponentproof · cited by 128
- IsCyclicstatement and proof · cited by 122
Cited by1
Results whose statement or proof uses this declaration.
- Group.isCyclic_of_coprime_card_kerproof · cited by 1