Corollary 4
Tag 05DI, permanent. Cite it as [Bourbaki, Tag 05DI].
Algebra, chapter I, § 6. Extensions, solvable groups, nilpotent groups
Let f: G' → G be a group homomorphism. Suppose that (a) G is nilpotent. (b) The homomorphism f₁: G'/(G', G') → G/(G, G), derived from f by passing to the quotients, is surjective. Then f is surjective.
This follows from Corollary 3 applied to the subgroup H = f(G').
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.