Theorems · Theorem · group theory
Nat.Prime.exists_orderOf_eq_pow_factorization_exponent
∀ (G : Type u) [inst : Monoid G] {p : ℕ}, Nat.Prime p → ∃ g, orderOf g = p ^ (Monoid.exponent G).factorization p- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- Bot.botproof · cited by 4,720
- Monoidstatement and proof · cited by 3,887
- Factproof · cited by 2,726
- mul_commproof · cited by 2,262
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- eq_or_neproof · cited by 1,117
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- orderOfstatement and proof · cited by 324
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.exists_orderOf_eq_exponentproof · cited by 1