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Theorems · Theorem · group theory

IsAddCyclic.card_nsmulAddMonoidHom_range

∀ (G : Type u_2) [inst : AddCommGroup G] [hG : IsAddCyclic G] [Finite G] (d : ℕ),
  Nat.card ↥(nsmulAddMonoidHom d).range = Nat.card G / (Nat.card G).gcd d
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic
Cited by
1 results in Mathlib
Foundations
Depth 98 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.index_nsmulAddMonoidHom_ker · cited by 1IsAddCyclic.index_nsmulAd…DFunLike.coe · cited by 62936DFunLike.coeAddCommGroup · cited by 12871AddCommGroupTop.top · cited by 9680Top.topAddSubgroup · cited by 3232AddSubgroupFinite · cited by 3029FiniteNat.card · cited by 844Nat.cardAddSubgroup.zmultiples · cited by 493AddSubgroup.zmultiplesaddOrderOf · cited by 208addOrderOfAddSubgroup.map · cited by 189AddSubgroup.mapAddMonoidHom.range · cited by 142AddMonoidHom.rangeIsAddCyclic · cited by 55IsAddCyclicnsmulAddMonoidHom · cited by 24nsmulAddMonoidHomAddMonoidHom.range_eq_map · cited by 15AddMonoidHom.range_eq_mapNat.card_zmultiples · cited by 11Nat.card_zmultiplesnsmulAddMonoidHom_apply · cited by 9nsmulAddMonoidHom_applyIsAddCyclic.card_nsmulAddMono…CITED BYCITES

Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.