Theorems · Theorem · group theory
AddSubgroup.lowerCentralSeries_isDescendingCentralSeries
∀ {G : Type u_1} [inst : AddGroup G], AddSubgroup.IsDescendingCentralSeries ⊤.lowerCentralSeriesThe lower central series of an additive group is a descending central series.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.lowerCentralSeriesstatement and proof · cited by 37
- AddSubgroup.mem_topproof · cited by 29
- AddSubgroup.addCommutator_mem_addCommutatorproof · cited by 9
- AddSubgroup.IsDescendingCentralSeriesstatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.lowerCentralSeries_length_eq_nilpotencyClassproof · cited by 4
- AddSubgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2