Theorems · Theorem · group theory
Subgroup.upperCentralSeries_isAscendingCentralSeries
∀ (G : Type u_1) [inst : Group G], Subgroup.IsAscendingCentralSeries (Subgroup.upperCentralSeries G)
The upper central series of a group is an ascending central series.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 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
- Subgroup.upperCentralSeriesstatement and proof · cited by 51
- Subgroup.IsAscendingCentralSeriesstatement · 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
- upperCentralSeries_isAscendingCentralSeriesproof · cited by 0