Theorems · Theorem · group theory
Group.nilpotencyClass_quotient_le
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [inst_1 : H.Normal] [_h : Group.IsNilpotent G],
Group.nilpotencyClass (G ⧸ H) ≤ Group.nilpotencyClass GThe nilpotency class of a quotient of G is less or equal the nilpotency class of G.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalstatement and proof · cited by 334
- QuotientGroup.mk'proof · cited by 90
- Group.IsNilpotentstatement and proof · cited by 80
- Group.nilpotencyClassstatement · cited by 47
- QuotientGroup.mk_surjectiveproof · cited by 12
- Group.nilpotencyClass_le_of_surjectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nilpotencyClass_quotient_leproof · cited by 0