Monoid.exponent_eq_prime_iff

∀ {G : Type u_1} [inst : Monoid G] [Nontrivial G] {p : ℕ},
  Nat.Prime p → (Monoid.exponent G = p ↔ ∀ (g : G), g ≠ 1 → orderOf g = p)

A nontrivial monoid has prime exponent p if and only if every non-identity element has order p.

Defined in: Mathlib.GroupTheory.Exponent
Cited by: 1 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid Nontrivial

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