Theorems · Definition · group theory
derivedSeries
(G : Type u_1) → [inst : Group G] → ℕ → Subgroup G
The derived series of the group G, obtained by starting from the subgroup ⊤ and repeatedly
taking the commutator of the previous subgroup with itself for n times.
- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by24
Results whose statement or proof uses this declaration.
- Group.isSolvable_of_ker_le_rangeproof · cited by 5
- Group.IsSolvable.casesOnstatement and proof · cited by 4
- Group.IsSolvable.commutator_lt_top_of_nontrivialproof · cited by 3
- derivedSeries_succstatement · cited by 3
- map_derivedSeries_le_derivedSeriesstatement and proof · cited by 2
- Equiv.Perm.not_isSolvable_fin_5proof · cited by 2
- not_isSolvable_of_mem_derivedSeriesstatement and proof · cited by 2
- Group.isSolvable_defstatement and proof · cited by 2
- derivedSeries_zerostatement · cited by 2
- Subgroup.derived_le_lower_centralstatement and proof · cited by 1
- IsSimpleGroup.derivedSeries_succstatement and proof · cited by 1
- Group.isSolvable_iff_commutator_ltproof · cited by 1