Theorems · Theorem · group theory
CharP.orderOf_eq_two_iff
∀ {R : Type u_6} [inst : Ring R] [Nontrivial R] [NoZeroDivisors R] (p : ℕ),
p ≠ 2 → ∀ [CharP R p] {x : R}, orderOf x = 2 ↔ x = -1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- NoZeroDivisorsstatement and proof · cited by 545
- CharPstatement and proof · cited by 478
- orderOfstatement · cited by 324
- ringChar.eqproof · cited by 6
- neg_one_eq_one_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrankproof · cited by 1