Theorems · Theorem · group theory
Subgroup.upperCentralSeries_nilpotencyClass
∀ {G : Type u_1} [inst : Group G] [hG : Group.IsNilpotent G],
Subgroup.upperCentralSeries G (Group.nilpotencyClass G) = ⊤- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsNilpotent
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Group.IsNilpotentstatement and proof · cited by 80
- Nat.find_specproof · cited by 74
- Subgroup.upperCentralSeriesstatement and proof · cited by 51
- Group.nilpotencyClassstatement · cited by 47
- Group.nilpotencyClass_defproof · cited by 5
- Group.IsNilpotent.nilpotentproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 5
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- upperCentralSeries_nilpotencyClassproof · cited by 0