Corollary 2

Tag 05E6, permanent. Cite it as [Bourbaki, Tag 05E6].

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

Let $f : G_1 \to G_2$ be a homomorphism of finite groups. For every Sylow p-subgroup $P_1$ of $G_1$ there exists a Sylow p-subgroup $P_2$ of $G_2$ such that $f(P_1) \subset P_2$ .

This follows from Theorem 3 (b) applied to the subgroup $f(P_1)$ of $G_2$ .

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

Cited by

Nothing.

Cites

Theorem 3