Theorems · Theorem · group theory
AddSubgroup.upperCentralSeries_nilpotencyClass
∀ {G : Type u_1} [inst : AddGroup G] [hG : AddGroup.IsNilpotent G],
AddSubgroup.upperCentralSeries G (AddGroup.nilpotencyClass G) = ⊤- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddGroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.find_specproof · cited by 74
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddSubgroup.upperCentralSeriesstatement and proof · cited by 32
- AddGroup.nilpotencyClassstatement · cited by 26
- AddGroup.IsNilpotent.nilpotentproof · cited by 5
- AddGroup.nilpotencyClass_defproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 4
- AddGroup.nilpotencyClass_quotient_centerproof · cited by 2