Theorems · Theorem · group theory
Subgroup.map_lowerCentralSeries
∀ {G : Type u_1} [inst : Group G] (S : Subgroup G) {K : Type u_2} [inst_1 : Group K] (f : G →* K) (n : ℕ),
Subgroup.map f (S.lowerCentralSeries n) = (Subgroup.map f S).lowerCentralSeries nThe lower central series commutes with images under a group homomorphism.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketproof · cited by 642
- Subgroup.mapstatement and proof · cited by 301
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- Subgroup.map_commutatorproof · cited by 12
- Subgroup.lowerCentralSeries_succproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.top_subtype_lowerCentralSeriesproof · cited by 4
- Group.nilpotencyClass_le_of_ker_le_centerproof · cited by 2
- Subgroup.isNilpotent_of_ker_le_centerproof · cited by 2
- Subgroup.lowerCentralSeries.mapproof · cited by 1