Theorems · Definition · group theory
CommGroup.freeRank
(G : Type u_1) → [inst : CommGroup G] → [Group.FG G] → ℕ
The free rank of a finitely generated abelian group is the rank of its free part.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- HasQuotient.Quotientproof · cited by 2,301
- CommGroupstatement and proof · cited by 990
- Group.FGstatement and proof · cited by 40
- Group.rankproof · cited by 20
- CommGroup.torsionproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- CommGroup.freeRank_eq_zerostatement · cited by 1
- CommGroup.freeRank_eq_zero_iffstatement · cited by 1
- CommGroup.freeRank_congrstatement · cited by 0
- CommGroup.freeRank_defstatement · cited by 0
- CommGroup.freeRank_eq_zero_of_finitestatement · cited by 0
- CommGroup.freeRank_ge_of_surjectivestatement · cited by 0