Theorems · Theorem · group theory
upperCentralSeriesStep_eq_comap_center
Deprecated since 2026-03-25Use Subgroup.upperCentralSeriesStep_eq_comap_center instead.
∀ {G : Type u_1} [inst : Group G] (N : Subgroup G) [inst_1 : N.Normal],
N.upperCentralSeriesStep = Subgroup.comap (QuotientGroup.mk' N) (Subgroup.center (G ⧸ N))Alias of Subgroup.upperCentralSeriesStep_eq_comap_center.
The proof that upperCentralSeriesStep N is the preimage of the centre of G/N under
the canonical surjection.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
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Cites9
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
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalstatement · cited by 334
- Subgroup.comapstatement · cited by 154
- Subgroup.centerstatement · cited by 121
- QuotientGroup.mk'statement · cited by 90
- Subgroup.upperCentralSeriesStepstatement · cited by 8
- Subgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 2
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