Theorems · Theorem · group theory
orderOf_eq_two_iff
∀ {G : Type u} [inst : Monoid G], Monoid.exponent G = 2 → ∀ {x : G}, orderOf x = 2 ↔ x ≠ 1- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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Cites6
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
- orderOfstatement and proof · cited by 324
- Monoid.exponentstatement and proof · cited by 128
- orderOf_oneproof · cited by 15
- Monoid.pow_exponent_eq_oneproof · cited by 13
- orderOf_eq_primeproof · cited by 5
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