Theorems · Theorem · group theory
AddGroup.nilpotencyClass_sum
∀ {G₁ : Type u_2} {G₂ : Type u_3} [inst : AddGroup G₁] [inst_1 : AddGroup G₂] [AddGroup.IsNilpotent G₁]
[AddGroup.IsNilpotent G₂],
AddGroup.nilpotencyClass (G₁ × G₂) = max (AddGroup.nilpotencyClass G₁) (AddGroup.nilpotencyClass G₂)The nilpotency class of a product is the max of the nilpotency classes of the factors.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- eq_of_forall_ge_iffproof · cited by 96
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddSubgroup.lowerCentralSeriesproof · cited by 37
- AddGroup.nilpotencyClassstatement · cited by 26
- max_le_iffproof · cited by 25
- AddSubgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 5
- AddSubgroup.top_lowerCentralSeries_sumproof · cited by 1
- AddSubgroup.prod_eq_bot_iffproof · cited by 1
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