Theorems · Definition · group theory
IsOfFinAddOrder.addGroupMultiples
{G : Type u_1} → [inst : AddMonoid G] → {x : G} → IsOfFinAddOrder x → AddGroup ↥(AddSubmonoid.multiples x)The additive submonoid generated by an element is an additive group if that element has finite order.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement · cited by 4,410
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- IsOfFinAddOrderstatement and proof · cited by 105
- AddSubmonoid.multiplesstatement · cited by 40
- IsOfFinAddOrder.exists_nsmul_eq_zeroproof · cited by 6
- AddSubmonoid.addGroupMultiplesproof · cited by 0
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