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Theorems · Theorem · group theory

IsAddCyclic.index_nsmulAddMonoidHom_ker

∀ (G : Type u_2) [inst : AddCommGroup G] [IsAddCyclic G] [Finite G] (d : ℕ),
  (nsmulAddMonoidHom 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
AddCommGroupIsAddCyclicFinite
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Around this declaration

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

IsAddCyclic.card_nsmulAddMonoidHom_ker · cited by 1IsAddCyclic.card_nsmulAdd…AddCommGroup · cited by 12871AddCommGroupFinite · cited by 3029FiniteNat.card · cited by 844Nat.cardAddMonoidHom.ker · cited by 158AddMonoidHom.kerAddSubgroup.index · cited by 104AddSubgroup.indexIsAddCyclic · cited by 55IsAddCyclicnsmulAddMonoidHom · cited by 24nsmulAddMonoidHomAddSubgroup.index_ker · cited by 3AddSubgroup.index_kerIsAddCyclic.card_nsmulAddMonoidHom_range · cited by 1IsAddCyclic.card_nsmulAdd…IsAddCyclic.index_nsmulAddMon…CITED BYCITES

Cites9

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Cited by1

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