Theorems · Theorem · group theory
AddSubgroup.upperCentralSeries_one
∀ (G : Type u_2) [inst : AddGroup G], AddSubgroup.upperCentralSeries G 1 = AddSubgroup.center G
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketproof · cited by 642
- AddSubgroup.extproof · cited by 75
- AddSubgroup.centerstatement · cited by 40
- AddSubgroup.upperCentralSeriesstatement · cited by 32
- add_neg_eq_zeroproof · cited by 20
- AddSubgroup.Characteristicproof · cited by 17
- AddSubmonoid.mk.congr_simpproof · cited by 14
- AddSubsemigroup.mk.congr_simpproof · cited by 14
- add_neg_eq_iff_eq_addproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.upperCentralSeries_zero_eq_top_iffproof · cited by 2
- AddSubgroup.comap_upperCentralSeries_quotient_centerproof · cited by 2
- AddGroup.IsNilpotent.center_ne_botproof · cited by 0
- AddCommGroup.nilpotencyClass_nonposproof · cited by 0