Corollary 2

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

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

Let $G$ be a nilpotent group and $H$ a subgroup of $G$ . If $H$ is distinct from $G$ , there exists a normal subgroup $N$ of $G$ , containing $H$ , distinct from $G$ and such that $G/N$ is commutative.

Let $k$ be the least index such that $H^k \neq G$ . The group $H^k$ satisfies the required conditions.

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

Cited by

Corollary 3, § 6

Cites

Nothing.