Theorems · Theorem · group theory
AddSubgroup.upperCentralSeries.card_image_eq_of_le_nilpotencyClass
∀ {G : Type u_1} [inst : AddGroup G] {a : ℕ},
a ≤ AddGroup.nilpotencyClass G → (AddSubgroup.upperCentralSeries G '' Set.Iic a).ncard = a + 1- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.imagestatement · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Set.Iicstatement · cited by 1,111
- Set.ncardstatement · cited by 344
- AddSubgroup.upperCentralSeriesstatement and proof · cited by 32
- AddGroup.nilpotencyClassstatement and proof · cited by 26
- StrictMonoOn.injOnproof · cited by 22
- Set.ncard_eq_of_bijectiveproof · cited by 2
- AddSubgroup.upperCentralSeries.StrictMonoOnproof · cited by 1
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