Theorems · Theorem · group theory
CommGroup.mem_torsion
∀ {G : Type u_1} [inst : CommGroup G] (g : G), g ∈ CommGroup.torsion G ↔ IsOfFinOrder g- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 44 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
- CommGroupstatement and proof · cited by 990
- IsOfFinOrderstatement · cited by 113
- CommGroup.torsionstatement · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.Units.rootsOfUnity_eq_torsionproof · cited by 2
- NumberField.Units.mem_torsionproof · cited by 2
- NumberField.Units.dvd_torsionOrder_of_isPrimitiveRootproof · cited by 1
- IsCyclotomicExtension.Rat.Three.Units.memproof · cited by 1
- NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrankproof · cited by 1
- NumberField.Units.rootsOfUnity_eq_oneproof · cited by 0