Theorems · Theorem · group theory
orderOf_dvd_natCard
∀ {G : Type u_6} [inst : Group G] (x : G), orderOf x ∣ Nat.card G- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Nat.cardstatement · cited by 844
- Infiniteproof · cited by 352
- orderOfstatement and proof · cited by 324
- Nat.card_eq_fintype_cardproof · cited by 200
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- fintypeOrInfiniteproof · cited by 14
Cited by14
Results whose statement or proof uses this declaration.
- pow_card_eq_one'proof · cited by 9
- Group.exponent_dvd_nat_cardproof · cited by 4
- NumberField.Units.even_torsionOrderproof · cited by 3
- IsPGroup.of_card_dvd_powproof · cited by 2
- NumberField.Units.dvd_torsionOrder_of_isPrimitiveRootproof · cited by 1
- MulDistribMulAction.toMonoidHomZModOfIsCyclic_applyproof · cited by 1
- Subgroup.orderOf_dvd_natCardproof · cited by 1
- pow_mod_natCardproof · cited by 1
- IsPGroup.smul_mul_inv_trivial_or_surjectiveproof · cited by 1
- NumberField.Units.rootsOfUnity_eq_oneproof · cited by 0
- zpow_mod_natCardproof · cited by 0
- modularCyclotomicCharacter.compproof · cited by 0