Theorems · Theorem · group theory
Group.IsSolvable.commutator_lt_of_ne_bot
∀ {G : Type u_1} [inst : Group G] [Group.IsSolvable G] {H : Subgroup G}, H ≠ ⊥ → ⁅H, H⁆ < H- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsSolvable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- Group.IsSolvablestatement and proof · cited by 46
- MonoidHom.range_eq_mapproof · cited by 37
- Subgroup.range_subtypeproof · cited by 28
- Subgroup.map_commutatorproof · cited by 12
- Group.IsSolvable.commutator_lt_top_of_nontrivialproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Group.isSolvable_iff_commutator_ltproof · cited by 1
- IsSolvable.commutator_lt_of_ne_botproof · cited by 0