Theorems · Theorem · group theory
nilpotencyClass_le_of_surjective
Deprecated since 2026-03-25Use Group.nilpotencyClass_le_of_surjective instead.
∀ {G : Type u_1} [inst : Group G] {G' : Type u_2} [inst_1 : Group G'] (f : G →* G'),
Function.Surjective ⇑f → ∀ [h : Group.IsNilpotent G], Group.nilpotencyClass G' ≤ Group.nilpotencyClass GAlias of Group.nilpotencyClass_le_of_surjective.
The nilpotency class of the range of a surjective homomorphism from a
nilpotent group is less or equal the nilpotency class of the domain.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroupGroup.IsNilpotent
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Groupstatement · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Group.IsNilpotentstatement · cited by 80
- Group.nilpotencyClassstatement · cited by 47
- Group.nilpotencyClass_le_of_surjectiveproof · cited by 2
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