Theorems · Definition · group theory
Subgroup.upperCentralSeriesAux
(G : Type u_1) → [inst : Group G] → ℕ → (H : Subgroup G) ×' H.Characteristic
An auxiliary type-theoretic definition defining both the upper central series of a group, and a proof that it is characteristic, all in one go.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 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.
Cites3
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
- Subgroupstatement · cited by 3,593
- Subgroup.Characteristicstatement · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.upperCentralSeriesproof · cited by 51
- Subgroup.upperCentralSeries_oneproof · cited by 7
- Subgroup.upperCentralSeries_monoproof · cited by 5
- Subgroup.upperCentralSeriesAux.eq_defstatement and proof · cited by 0
- upperCentralSeriesAuxproof · cited by 0
- Subgroup.upperCentralSeries.eq_defstatement · cited by 0