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Theorems · Theorem · group theory

IsCyclic.index_powMonoidHom_ker

∀ (G : Type u_2) [inst : CommGroup G] [IsCyclic G] [Finite G] (d : ℕ),
  (powMonoidHom d).ker.index = Nat.card G / (Nat.card G).gcd d
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic
Cited by
1 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroupIsCyclicFinite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsCyclic.card_powMonoidHom_ker · cited by 1IsCyclic.card_powMonoidHo…Finite · cited by 3029FiniteCommGroup · cited by 990CommGroupNat.card · cited by 844Nat.cardMonoidHom.ker · cited by 212MonoidHom.kerSubgroup.index · cited by 150Subgroup.indexIsCyclic · cited by 122IsCyclicpowMonoidHom · cited by 35powMonoidHomSubgroup.index_ker · cited by 7Subgroup.index_kerIsCyclic.card_powMonoidHom_range · cited by 1IsCyclic.card_powMonoidHo…IsCyclic.index_powMonoidHom_k…CITED BYCITES

Cites9

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Cited by1

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