Theorems · Theorem · group theory
CommGroup.freeRank_eq_zero_iff
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : Group.FG G], CommGroup.freeRank G = 0 ↔ IsMulTorsion G- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommGroupstatement and proof · cited by 990
- Group.FGstatement and proof · cited by 40
- IsMulTorsionstatement and proof · cited by 35
- CommGroup.freeRankstatement · cited by 6
- Group.rank_eq_zero_iffproof · cited by 2
- QuotientGroup.subsingleton_iffproof · cited by 1
- CommGroup.torsion_eq_top_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CommGroup.freeRank_eq_zeroproof · cited by 1