Theorems · Theorem · group theory
IsAddTorsion.exponentExists
∀ {G : Type u_1} [inst : AddGroup G],
IsAddTorsion G → (Set.range fun g => addOrderOf g).Finite → AddMonoid.ExponentExists GThe group exponent exists for any bounded torsion additive group.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- AddGroupstatement and proof · cited by 4,410
- Set.Finitestatement and proof · cited by 1,814
- addOrderOfstatement and proof · cited by 208
- IsAddTorsionstatement and proof · cited by 42
- AddMonoid.ExponentExistsstatement · cited by 17
- IsOfFinAddOrder.addOrderOf_posproof · cited by 16
- AddMonoid.exponent_ne_zeroproof · cited by 4
- AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finiteproof · cited by 3
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