Theorems · Theorem · group theory
orderOf_neg_one
∀ {R : Type u_6} [inst : Ring R] [Nontrivial R], orderOf (-1) = if ringChar R = 2 then 1 else 2- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- one_powproof · cited by 521
- orderOfstatement and proof · cited by 324
- Even.neg_powproof · cited by 99
- ringCharstatement and proof · cited by 73
- orderOf_oneproof · cited by 15
- orderOf_eq_primeproof · cited by 5
- neg_one_eq_one_iffproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Nat.totient_evenproof · cited by 4
- IsPrimitiveRoot.neg_oneproof · cited by 3
- NumberField.Units.even_torsionOrderproof · cited by 3
- NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_ltproof · cited by 2
- IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrderproof · cited by 1