Theorems · Theorem · group theory
exists_nsmul_eq_self_of_coprime
∀ {G : Type u_1} [inst : AddMonoid G] {x : G} {n : ℕ}, n.Coprime (addOrderOf x) → ∃ m, m • n • x = x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- addOrderOfstatement and proof · cited by 208
- nsmul_zeroproof · cited by 73
- one_nsmulproof · cited by 63
- mul_nsmulproof · cited by 24
- mod_addOrderOf_nsmulproof · cited by 7
- AddMonoid.addOrderOf_eq_one_iffproof · cited by 6
- Nat.exists_mul_mod_eq_one_of_coprimeproof · cited by 4
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