Theorems · Theorem · group theory
Subgroup.upperCentralSeriesStep_eq_comap_center
∀ {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))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
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- HasQuotient.Quotientstatement and proof · cited by 2,301
- mul_assocproof · cited by 1,667
- div_eq_mul_invproof · cited by 715
- Bracket.bracketproof · cited by 642
- Subgroup.Normalstatement and proof · cited by 334
- mul_inv_revproof · cited by 270
- QuotientGroup.mkproof · cited by 196
- Subgroup.comapstatement · cited by 154
- Subgroup.centerstatement · cited by 121
- Subgroup.extproof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.comap_upperCentralSeries_quotient_centerproof · cited by 3
- upperCentralSeriesStep_eq_comap_centerproof · cited by 0