Theorems · Theorem · group theory
not_isMulTorsion_iff
∀ (G : Type u_1) [inst : Monoid G], ¬IsMulTorsion G ↔ ∃ g, ¬IsOfFinOrder g
A monoid is not a torsion monoid if it has an element of infinite order.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- IsOfFinOrderstatement · cited by 113
- IsMulTorsionstatement · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.not_isTorsion_iffproof · cited by 0