Theorems · Theorem · group theory
AddCommGroup.finite_of_fg_isAddTorsion
∀ (G : Type u) [inst : AddCommGroup G] [hG' : AddGroup.FG G], IsAddTorsion G → Finite G
- Defined in
- Mathlib.GroupTheory.FiniteAbelian.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupAddGroup.FG
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Finitestatement · cited by 3,029
- IsAddTorsionstatement and proof · cited by 42
- AddGroup.FGstatement and proof · cited by 37
- isAddTorsion_iff_isTorsion_intproof · cited by 2
- Module.finite_of_fg_torsionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.finiteIndex_range_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddCommGroup.finite_of_fg_torsionproof · cited by 0