Theorems · Theorem · group theory
Monoid.exponent_ne_zero_iff_range_orderOf_finite
∀ {G : Type u} [inst : Monoid G], (∀ (g : G), 0 < orderOf g) → (Monoid.exponent G ≠ 0 ↔ (Set.range orderOf).Finite)- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Monoidstatement and proof · cited by 3,887
- Finset.prodproof · cited by 2,356
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.ne'proof · cited by 1,417
- Set.mem_range_selfproof · cited by 328
- orderOfstatement and proof · cited by 324
- Monoid.exponentstatement and proof · cited by 128
- Finset.mem_coeproof · cited by 91
Cited by3
Results whose statement or proof uses this declaration.
- Monoid.exponent_eq_zero_iff_range_orderOf_infiniteproof · cited by 1
- IsMulTorsion.exponentExistsproof · cited by 1
- Monoid.exists_orderOf_eq_exponentproof · cited by 1