Theorems · Theorem · group theory
Subgroup.nilpotencyClass_le
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [hG : Group.IsNilpotent G],
Group.nilpotencyClass ↥H ≤ Group.nilpotencyClass GThe nilpotency class of a subgroup is less or equal to the nilpotency class of the group.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsNilpotent
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- le_topproof · cited by 411
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- eq_bot_iffproof · cited by 159
- Nat.findproof · cited by 139
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.lowerCentralSeriesproof · cited by 57
- Group.nilpotencyClassstatement and proof · cited by 47
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