Theorems · Theorem · group theory
Subgroup.upperCentralSeries_one
∀ (G : Type u_1) [inst : Group G], Subgroup.upperCentralSeries G 1 = Subgroup.center G
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketproof · cited by 642
- Subgroup.centerstatement · cited by 121
- Subgroup.extproof · cited by 108
- Subgroup.upperCentralSeriesstatement · cited by 51
- mul_inv_eq_oneproof · cited by 20
- Subgroup.Characteristicproof · cited by 20
- Submonoid.mk.congr_simpproof · cited by 14
- Subsemigroup.mk.congr_simpproof · cited by 14
- mul_inv_eq_iff_eq_mulproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.comap_upperCentralSeries_quotient_centerproof · cited by 3
- Subgroup.upperCentralSeries_one_eq_top_iffproof · cited by 2
- CommGroup.nilpotencyClass_le_oneproof · cited by 1
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- upperCentralSeries_oneproof · cited by 0
- Group.IsNilpotent.center_ne_botproof · cited by 0
- Group.IsPerfect.center_quotient_center_eq_botproof · cited by 0