Theorems · Definition · group theory
addOrderOf
{G : Type u_1} → [AddMonoid G] → G → ℕaddOrderOf a is the order of the element a, i.e. the n ≥ 1, s.t. n • a = 0 if it
exists. Otherwise, i.e. if a is of infinite order, then addOrderOf a is 0 by convention.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 208 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 181 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- Function.minimalPeriodproof · cited by 100
Cited by220
Results whose statement or proof uses this declaration.
- addOrderOf_dvd_iff_nsmul_eq_zerostatement and proof · cited by 17
- IsOfFinAddOrder.addOrderOf_posstatement · cited by 16
- Nat.card_zmultiplesstatement · cited by 11
- addOrderOf_nsmul_eq_zerostatement and proof · cited by 11
- AddMonoid.addOrder_dvd_exponentstatement · cited by 10
- addOrderOf_pos_iffstatement and proof · cited by 10
- AddMonoid.minOrderproof · cited by 9
- approxAddOrderOfproof · cited by 9
- addOrderOf_eq_zero_iffstatement and proof · cited by 9
- addOrderOf_eq_card_of_forall_mem_zmultiplesstatement · cited by 8
- addOrderOf_zerostatement · cited by 8
- finEquivMultiplesstatement and proof · cited by 7
Showing the 200 most cited of 220.