Theorems · Theorem · group theory
nilpotent_iff_lowerCentralSeries
Deprecated since 2026-03-25Use Subgroup.nilpotent_iff_lowerCentralSeries instead.
∀ {G : Type u_1} [inst : Group G], Group.IsNilpotent G ↔ ∃ n, ⊤.lowerCentralSeries n = ⊥Alias of Subgroup.nilpotent_iff_lowerCentralSeries.
A group is nilpotent if and only if its lower central series eventually reaches
the trivial subgroup.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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- Top.topstatement · cited by 9,680
- Groupstatement · cited by 6,238
- Bot.botstatement · cited by 4,720
- Subgroupstatement · cited by 3,593
- Group.IsNilpotentstatement · cited by 80
- Subgroup.lowerCentralSeriesstatement · cited by 57
- Subgroup.nilpotent_iff_lowerCentralSeriesproof · cited by 9
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