Theorems · Theorem · group theory
AddSubgroup.lowerCentralSeries_succ_eq_bot
∀ {G : Type u_1} [inst : AddGroup G] (S : AddSubgroup G) {n : ℕ},
S.lowerCentralSeries n ≤ AddSubgroup.center G → S.lowerCentralSeries (n + 1) = ⊥- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- add_assocproof · cited by 746
- Bracket.bracketproof · cited by 642
- neg_add_revproof · cited by 236
- AddSubgroup.centerstatement and proof · cited by 40
- AddSubgroup.lowerCentralSeriesstatement and proof · cited by 37
- add_neg_eq_zeroproof · cited by 20
- Set.subset_singleton_iffproof · cited by 12
- addCommutatorElement_defproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_le_of_ker_le_centerproof · cited by 1
- AddSubgroup.isNilpotent_of_ker_le_centerproof · cited by 1