Corollary 3

Tag 05D5, permanent. Cite it as [Bourbaki, Tag 05D5].

Algebra, chapter I, § 6. Extensions, solvable groups, nilpotent groups

Let H be a subgroup of G. The following conditions are equivalent:

(i) $H \supset D(G)$ ; (ii) H is a normal subgroup and $G/H$ is commutative. (ii) $\Rightarrow$ (i) by Corollary 2 and (i) $\Rightarrow$ (ii) by § 4, no. 7, Theorem 4, since every subgroup of a commutative group is normal.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Example, § 6
Proposition 12, § 6
Corollary 4, § 6

Cites

§ 4, no. 7, Theorem 4
Corollary 2