Theorems · Theorem · group theory
Monoid.exponent_eq_zero_of_order_zero
∀ {G : Type u} [inst : Monoid G] {g : G}, orderOf g = 0 → Monoid.exponent G = 0- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 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.
Cites7
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
- LT.lt.ne'proof · cited by 1,417
- orderOfstatement and proof · cited by 324
- Monoid.exponentstatement · cited by 128
- Monoid.ExponentExistsproof · cited by 18
- Monoid.exponent_eq_zero_iffproof · cited by 5
- Monoid.ExponentExists.orderOf_posproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- DihedralGroup.exponentproof · cited by 1
- Monoid.exponent_eq_iSup_orderOf'proof · cited by 0
- IsCyclic.exponent_eq_zero_of_infiniteproof · cited by 0
- QuaternionGroup.exponentproof · cited by 0