Theorems · Inductive type · group theory
Group.IsSolvable
(G : Type u_1) → [Group G] → Prop
A group G is solvable if its derived series is eventually trivial. We use this definition
because it's the most convenient one to work with.
- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
Cited by49
Results whose statement or proof uses this declaration.
- Group.isSolvable_of_ker_le_rangestatement and proof · cited by 5
- Group.IsSolvable.casesOnstatement and proof · cited by 4
- Group.isSolvable_of_commstatement · cited by 4
- Group.isSolvable_of_isSolvable_injectivestatement and proof · cited by 4
- Group.isSolvable_of_surjectivestatement and proof · cited by 4
- Group.IsSolvable.commutator_lt_top_of_nontrivialstatement and proof · cited by 3
- gal_X_pow_isSolvablestatement · cited by 2
- Equiv.Perm.not_isSolvable_fin_5statement · cited by 2
- not_isSolvable_of_mem_derivedSeriesstatement · cited by 2
- Group.isSolvable_defstatement and proof · cited by 2
- Group.IsSolvable.commutator_lt_of_ne_botstatement and proof · cited by 2
- isSolvable_gal_minpolystatement and proof · cited by 2