Theorems · Theorem · group theory
Group.rank_spec
∀ (G : Type u_1) [inst : Group G] [h : Group.FG G], ∃ S, S.card = Group.rank G ∧ Subgroup.closure ↑S = ⊤
- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 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.
- Finsetstatement · cited by 13,712
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Finset.cardstatement · cited by 2,327
- Subgroup.closurestatement · cited by 196
- Nat.find_specproof · cited by 74
- Group.FGstatement and proof · cited by 40
- Group.rankstatement · cited by 20
- Group.fg_iff'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Group.rank_le_of_surjectiveproof · cited by 3
- Group.rank_eq_zero_iffproof · cited by 2
- Subgroup.rank_le_index_mul_rankproof · cited by 1
- Subgroup.index_center_le_powproof · cited by 1
- card_dvd_exponent_pow_rankproof · cited by 1