Theorems · Theorem · group theory
Subgroup.self_le_normalizer_lowerCentralSeries
∀ {G : Type u_1} [inst : Group G] (S : Subgroup G) (n : ℕ), S ≤ Subgroup.normalizer ↑(S.lowerCentralSeries n)- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.normalizerstatement and proof · cited by 108
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- Subgroup.le_normalizerproof · cited by 19
- Subgroup.lowerCentralSeries_succproof · cited by 5
- Subgroup.normalizer_commutator_ge_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_antitoneproof · cited by 3