Theorems · Definition · group theory
upperCentralSeriesStep
Deprecated since 2026-03-25Use Subgroup.upperCentralSeriesStep instead.
{G : Type u_1} → [inst : Group G] → (N : Subgroup G) → [N.Normal] → Subgroup GAlias of Subgroup.upperCentralSeriesStep.
If N is a normal subgroup of G, then the set {x : G | ∀ y : G, x*y*x⁻¹*y⁻¹ ∈ N}
is a subgroup of G (because it is the preimage in G of the centre of the
quotient group G/N.)
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext
- Assumes
- GroupSubgroup.Normal
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- Groupstatement · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.Normalstatement · cited by 334
- Subgroup.upperCentralSeriesStepproof · cited by 8
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