Theorems · Theorem · group theory
IsCyclic.card_powMonoidHom_ker
∀ (G : Type u_2) [inst : CommGroup G] [IsCyclic G] [Finite G] (d : ℕ), Nat.card ↥(powMonoidHom 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.
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- CommGroupstatement and proof · cited by 990
- Nat.cardstatement and proof · cited by 844
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.indexproof · cited by 150
- IsCyclicstatement and proof · cited by 122
- powMonoidHomstatement and proof · cited by 35
- mul_left_inj'proof · cited by 35
- Subgroup.card_mul_indexproof · cited by 16
- Subgroup.index_ne_zero_of_finiteproof · cited by 5
- IsCyclic.index_powMonoidHom_kerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclic.index_powMonoidHom_rangeproof · cited by 2