Theorems · Theorem · group theory
Group.isSolvable_iff_commutator_lt
∀ {G : Type u_1} [inst : Group G] [WellFoundedLT (Subgroup G)],
Group.IsSolvable G ↔ ∀ (H : Subgroup G), H ≠ ⊥ → ⁅H, H⁆ < H- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- eq_or_neproof · cited by 1,117
- Bracket.bracketstatement and proof · cited by 642
- WellFoundedLTstatement and proof · cited by 491
- MonoidHom.rangeproof · cited by 314
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- Group.IsSolvablestatement and proof · cited by 46
- MonoidHom.range_eq_mapproof · cited by 37
Cited by1
Results whose statement or proof uses this declaration.
- isSolvable_iff_commutator_ltproof · cited by 0