Bourbaki

Corollary

Tag 0A5J, permanent. Cite it as [Bourbaki, Tag 0A5J].

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

⋂n⩾1CnF(X)={e}. \bigcap_{n \geqslant 1} C^n F(X) = \{e\}.

Applying Theorem 2 with K = \mathbf{Z} and r = 0,

⋂n⩾1CnF(X)=⋂n⩾1g−1(1+A^n(X))=g−1(⋂n⩾1(1+A^n(X)))=g−1(1)={e}. \bigcap_{n \geqslant 1} C^n F(X) = \bigcap_{n \geqslant 1} g^{-1}(1 + \hat{A}_n(X)) = g^{-1}\left(\bigcap_{n \geqslant 1} (1 + \hat{A}_n(X))\right) = g^{-1}(1) = \{e\}.

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

Cited by

Nothing.

Cites

Transcribed from the printed volume. Not translated.