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Theorems · Theorem · group theory

Group.nilpotent_of_mulEquiv

∀ {G : Type u_1} [inst : Group G] {G' : Type u_2} [inst_1 : Group G'] [_h : Group.IsNilpotent G] (f : G ≃* G'),
  Group.IsNilpotent G'

Nilpotency respects isomorphisms.

Defined in
Mathlib.GroupTheory.Nilpotent
Cited by
2 results in Mathlib
Foundations
Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupGroupGroup.IsNilpotent
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Group.isNilpotent_of_product_of_sylow_group · cited by 2Group.isNilpotent_of_prod…nilpotent_of_mulEquiv · cited by 0nilpotent_of_mulEquivGroup · cited by 6238GroupMulEquiv · cited by 1142MulEquivMulEquiv.toMonoidHom · cited by 126MulEquiv.toMonoidHomGroup.IsNilpotent · cited by 80Group.IsNilpotentMulEquiv.surjective · cited by 41MulEquiv.surjectiveGroup.nilpotent_of_surjective · cited by 3Group.nilpotent_of_surjec…Group.nilpotent_of_mulEquivCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.