Theorems · Definition · group theory
CommGroup.torsion
(G : Type u_1) → [inst : CommGroup G] → Subgroup G
The torsion subgroup of an abelian group.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- Submonoidproof · cited by 3,086
- CommGroupstatement and proof · cited by 990
- CommMonoid.torsionproof · cited by 12
Cited by18
Results whose statement or proof uses this declaration.
- NumberField.Units.torsionproof · cited by 53
- CommGroup.mem_torsionstatement · cited by 6
- CommGroup.freeRankproof · cited by 6
- CommGroup.le_comap_torsionstatement · cited by 2
- NumberField.Units.rootsOfUnity_eq_torsionproof · cited by 2
- CommGroup.torsion_eq_top_iffstatement and proof · cited by 1
- CommGroup.comap_torsion_of_injectivestatement · cited by 1
- MulEquiv.comap_torsionstatement · cited by 1
- CommGroup.finite_torsion_of_descentstatement · cited by 1
- MulEquiv.map_torsionstatement and proof · cited by 1
- CommGroup.map_torsion_lestatement · cited by 0
- CommGroup.isMulTorsionFree_iff_torsion_eq_botstatement and proof · cited by 0