Theorems · Theorem · group theory
mem_upperCentralSeriesStep
Deprecated since 2026-03-25Use Subgroup.mem_upperCentralSeriesStep instead.
∀ {G : Type u_1} [inst : Group G] (N : Subgroup G) [inst_1 : N.Normal] (x : G),
x ∈ N.upperCentralSeriesStep ↔ ∀ (y : G), ⁅x, y⁆ ∈ NAlias of Subgroup.mem_upperCentralSeriesStep.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext
- Assumes
- GroupSubgroup.Normal
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
- Subgroupstatement · cited by 3,593
- Bracket.bracketstatement · cited by 642
- Subgroup.Normalstatement · cited by 334
- commutatorElementstatement · cited by 41
- Subgroup.upperCentralSeriesStepstatement · cited by 8
- Subgroup.mem_upperCentralSeriesStepproof · cited by 1
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