Theorems · Theorem · group theory
Subgroup.mem_upperCentralSeriesStep
∀ {G : Type u_1} [inst : Group G] (N : Subgroup G) [inst_1 : N.Normal] (x : G),
x ∈ N.upperCentralSeriesStep ↔ ∀ (y : G), ⁅x, y⁆ ∈ N- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement · cited by 642
- Subgroup.Normalstatement and proof · cited by 334
- commutatorElementstatement · cited by 41
- Subgroup.upperCentralSeriesStepstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- mem_upperCentralSeriesStepproof · cited by 0