Theorems · Theorem · group theory
Monoid.not_isTorsion_iff
Deprecated since 2026-07-01Use not_isMulTorsion_iff instead.
∀ (G : Type u_1) [inst : Monoid G], ¬IsMulTorsion G ↔ ∃ g, ¬IsOfFinOrder g
Alias of not_isMulTorsion_iff.
A monoid is not a torsion monoid if it has an element of infinite order.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement · cited by 3,887
- IsOfFinOrderstatement · cited by 113
- IsMulTorsionstatement · cited by 35
- not_isMulTorsion_iffproof · cited by 1
Cited by0
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