Theorems · Theorem · group theory
Subgroup.lowerCentralSeries_isDescendingCentralSeries
∀ {G : Type u_1} [inst : Group G], Subgroup.IsDescendingCentralSeries ⊤.lowerCentralSeriesThe lower central series of a group is a descending central series.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites7
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 · cited by 3,593
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- Subgroup.mem_topproof · cited by 20
- Subgroup.IsDescendingCentralSeriesstatement · cited by 14
- Subgroup.commutator_mem_commutatorproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_length_eq_nilpotencyClassproof · cited by 5
- Subgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2
- lowerCentralSeries_isDescendingCentralSeriesproof · cited by 0