Theorem 1

Tag 0A5D, permanent. Cite it as [Bourbaki, Tag 0A5D].

Lie Groups and Lie Algebras, chapter II, § 5. Magnus algebras

Let $r$ be a mapping of $\mathbf{X}$ into $\hat{\mathbf{A}}(\mathbf{X})$ such that $\omega(r(x)) \geq 2$ for all $x \in \mathbf{X}$ . The unique homomorphism $g$ of the free group $F(\mathbf{X})$ into the Magnus group $\Gamma(\mathbf{X})$ such that $g(x) = 1 + x + r(x)$ for all $x \in \mathbf{X}$ is injective.

We first prove three lemmas.

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

Cited by

§ 5. Magnus algebras
Lemma 4, § 5
Remark, § 6

Cites

Nothing.