Theorems · Theorem · group theory
orderOf_units
∀ {G : Type u_1} [inst : Monoid G] {y : Gˣ}, orderOf ↑y = orderOf y- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- orderOfstatement · cited by 324
- Units.coeHomproof · cited by 44
- Units.val_injectiveproof · cited by 17
- orderOf_injectiveproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.autToPow_specproof · cited by 5
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- Nat.totient_evenproof · cited by 4
- NumberField.Units.even_torsionOrderproof · cited by 3
- orderOf_lt_cardproof · cited by 1
- NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrankproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- FiniteField.card_cast_subgroup_card_ne_zeroproof · cited by 0
- minpoly_algHom_toLinearMapproof · cited by 0