Theorems · Theorem · group theory
AddSubgroup.lowerCentralSeries_antitone
∀ {G : Type u_1} [inst : AddGroup G] (S : AddSubgroup G), Antitone S.lowerCentralSeries- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Antitonestatement · cited by 563
- AddSubgroup.lowerCentralSeriesstatement and proof · cited by 37
- antitone_nat_of_succ_leproof · cited by 21
- AddSubgroup.lowerCentralSeries_succproof · cited by 4
- AddSubgroup.self_le_normalizer_lowerCentralSeriesproof · cited by 1
- AddSubgroup.le_normalizer_iff_addCommutator_le_leftproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 5
- AddSubgroup.lowerCentralSeries_le_selfproof · cited by 0