Theorems · Theorem · group theory
ascending_central_series_le_upper
Deprecated since 2026-03-25Use Subgroup.ascending_central_series_le_upper instead.
∀ {G : Type u_1} [inst : Group G] (H : ℕ → Subgroup G),
Subgroup.IsAscendingCentralSeries H → ∀ (n : ℕ), H n ≤ Subgroup.upperCentralSeries G nAlias of Subgroup.ascending_central_series_le_upper.
Any ascending central series for a group is bounded above by the upper central series.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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- Groupstatement · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.upperCentralSeriesstatement · cited by 51
- Subgroup.IsAscendingCentralSeriesstatement · cited by 14
- Subgroup.ascending_central_series_le_upperproof · cited by 3
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