Theorems · Definition · group theory
AddGroup.rank
(G : Type u_1) → [inst : AddGroup G] → [h : AddGroup.FG G] → ℕ
The minimum number of generators of an additive group.
- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddGroup.FG
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.
- AddGroupstatement and proof · cited by 4,410
- Nat.findproof · cited by 139
- AddGroup.FGstatement and proof · cited by 37
Cited by15
Results whose statement or proof uses this declaration.
- AddCommGroup.freeRankproof · cited by 6
- AddGroup.rank_lestatement · cited by 3
- AddGroup.rank_le_of_surjectivestatement and proof · cited by 3
- AddGroup.rank_specstatement · cited by 3
- AddGroup.rank_eq_zero_iffstatement and proof · cited by 2
- AddSubgroup.rank_closure_finset_le_cardstatement · cited by 1
- AddSubgroup.rank_congrstatement and proof · cited by 1
- AddGroup.rank_congrstatement · cited by 1
- AddGroup.rank_eq_zerostatement and proof · cited by 1
- card_dvd_exponent_nsmul_rankstatement and proof · cited by 1
- AddCommGroup.freeRank_defstatement · cited by 0
- AddGroup.rank_posstatement and proof · cited by 0