Theorems · Theorem · group theory
exists_pow_eq_self_of_coprime
∀ {G : Type u_1} [inst : Monoid G] {x : G} {n : ℕ}, n.Coprime (orderOf x) → ∃ m, (x ^ n) ^ m = x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 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.
Cites8
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
- pow_oneproof · cited by 894
- one_powproof · cited by 521
- orderOfstatement and proof · cited by 324
- pow_mulproof · cited by 210
- orderOf_eq_one_iffproof · cited by 12
- pow_mod_orderOfproof · cited by 12
- Nat.exists_mul_mod_eq_one_of_coprimeproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.support_pow_coprimeproof · cited by 2
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
- Equiv.Perm.closure_cycle_coprime_swapproof · cited by 1