Theorems · Theorem · group theory
least_descending_central_series_length_eq_nilpotencyClass
Deprecated since 2026-03-25Use Subgroup.least_descending_central_series_length_eq_nilpotencyClass instead.
∀ {G : Type u_1} [inst : Group G] [hG : Group.IsNilpotent G], Nat.find ⋯ = Group.nilpotencyClass GAlias of Subgroup.least_descending_central_series_length_eq_nilpotencyClass.
The nilpotency class of a nilpotent G is equal to the smallest n for which the descending
central series reaches ⊥ in its n-th term.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsNilpotent
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement · cited by 3,593
- Nat.findstatement · cited by 139
- Group.IsNilpotentstatement · cited by 80
- Group.nilpotencyClassstatement · cited by 47
- Subgroup.IsDescendingCentralSeriesstatement · cited by 14
- Subgroup.nilpotent_iff_finite_descending_central_seriesstatement · cited by 4
- Subgroup.least_descending_central_series_length_eq_nilpotencyClassproof · cited by 2
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