Theorems · Definition · group theory
AddMonoid.minOrder
(α : Type u_2) → [AddMonoid α] → ℕ∞
The minimum order of a non-identity element. Also the minimum size of a nontrivial
subgroup, see AddMonoid.le_minOrder_iff_forall_addSubgroup. Returns ∞ if the monoid is
torsion-free.
- Defined in
- Mathlib.GroupTheory.Order.Min
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- AddMonoidstatement and proof · cited by 2,864
- iInfproof · cited by 1,690
- addOrderOfproof · cited by 208
- IsOfFinAddOrderproof · cited by 105
Cited by9
Results whose statement or proof uses this declaration.
- AddMonoid.le_minOrderstatement · cited by 2
- AddMonoid.le_minOrder_iff_forall_addSubgroupstatement · cited by 2
- AddMonoid.minOrder_le_natCardstatement · cited by 2
- cauchy_davenport_minOrder_addstatement and proof · cited by 2
- AddMonoid.minOrder_eq_topstatement · cited by 1
- ZMod.minOrderstatement · cited by 1
- ZMod.minOrder_of_primestatement · cited by 1
- AddMonoid.minOrder_eq_top_iffstatement · cited by 0
- AddMonoid.minOrder_le_addOrderOfstatement · cited by 0