Theorems · Theorem · group theory
AddGroup.isAddCyclic_of_coprime_card_ker
∀ {M : Type u_4} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddGroup N] (f : M →+ N),
(Nat.card ↥f.ker).Coprime (Nat.card N) →
∀ [IsAddCyclic ↥f.ker] [hN : IsAddCyclic N], Function.Surjective ⇑f → IsAddCyclic 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Nat.cardstatement and proof · cited by 844
- AddMonoidHom.kerstatement and proof · cited by 158
- IsAddCyclicstatement and proof · cited by 55
- AddMonoidHom.range_eq_topproof · cited by 20
- AddSubgroup.card_topproof · cited by 3
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.isAddCyclic_prod_iffproof · cited by 0