Theorems · Theorem · group theory
Subgroup.top_subtype_lowerCentralSeries
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) (n : ℕ),
Subgroup.map H.subtype (⊤.lowerCentralSeries n) = H.lowerCentralSeries nThe lower central series of H : Subgroup G computed in the ambient group G coincides with
the lower central series of H viewed as its own group, mapped back to G.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 74 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- Subgroup.subtypestatement and proof · cited by 185
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- MonoidHom.range_eq_mapproof · cited by 37
- Subgroup.map_lowerCentralSeriesproof · cited by 4
- Subgroup.subtype_rangeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2
- Subgroup.lowerCentralSeries_map_subtype_leproof · cited by 1
- Subgroup.lowerCentralSeries_eq_bot_of_nilpotencyClass_leproof · cited by 0
- Subgroup.nilpotencyClass_leproof · cited by 0