Theorems · Theorem · group theory
IsAddCyclic.card_nsmulAddMonoidHom_ker
∀ (G : Type u_2) [inst : AddCommGroup G] [IsAddCyclic G] [Finite G] (d : ℕ), Nat.card ↥(nsmulAddMonoidHom d).ker = (Nat.card G).gcd d
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- AddMonoidHom.kerstatement and proof · cited by 158
- AddSubgroup.indexproof · cited by 104
- IsAddCyclicstatement and proof · cited by 55
- mul_left_inj'proof · cited by 35
- nsmulAddMonoidHomstatement and proof · cited by 24
- AddSubgroup.card_mul_indexproof · cited by 7
- AddSubgroup.index_ne_zero_of_finiteproof · cited by 4
- IsAddCyclic.index_nsmulAddMonoidHom_kerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsAddCyclic.index_nsmulAddMonoidHom_rangeproof · cited by 0