Theorems · Theorem · group theory
orderOf_eq_prime
∀ {G : Type u_1} [inst : Monoid G] {x : G} {p : ℕ} [hp : Fact (Nat.Prime p)], x ^ p = 1 → x ≠ 1 → orderOf x = pThe backward direction of orderOf_eq_prime_iff.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- orderOfstatement · cited by 324
- orderOf_eq_prime_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- exists_prime_orderOf_dvd_cardproof · cited by 5
- orderOf_neg_oneproof · cited by 5
- DihedralGroup.orderOf_srproof · cited by 1
- mul_notMem_of_exponent_twoproof · cited by 1
- orderOf_eq_two_iffproof · cited by 0