Theorems · Theorem · group theory
Subgroup.ascending_central_series_le_upper
∀ {G : Type u_1} [inst : Group G] (H : ℕ → Subgroup G),
Subgroup.IsAscendingCentralSeries H → ∀ (n : ℕ), H n ≤ Subgroup.upperCentralSeries G nAny ascending central series for a group is bounded above by the upper central series.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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.
Cites4
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 and proof · cited by 3,593
- Subgroup.upperCentralSeriesstatement · cited by 51
- Subgroup.IsAscendingCentralSeriesstatement and proof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.nilpotent_iff_finite_ascending_central_seriesproof · cited by 4
- Subgroup.least_ascending_central_series_length_eq_nilpotencyClassproof · cited by 2
- ascending_central_series_le_upperproof · cited by 0