Theorems · Theorem · group theory
Subgroup.rank_commutator_le_card
∀ (G : Type u_1) [inst : Group G] [inst_1 : Finite ↑(commutatorSet G)], Group.rank ↥(commutator G) ≤ Nat.card ↑(commutatorSet G)
- Defined in
- Mathlib.GroupTheory.Commutator.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- commutatorstatement · cited by 56
- commutatorSetstatement and proof · cited by 20
- Group.rankstatement · cited by 20
- commutator_eq_closureproof · cited by 7
- Subgroup.rank_closure_finite_le_nat_cardproof · cited by 2
- Subgroup.rank_congrproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.card_commutator_dvd_index_center_powproof · cited by 1