Remark 2

Tag 0AT6, permanent. Cite it as [Bourbaki, Tag 0AT6].

Lie Groups and Lie Algebras, chapter V, § 5. Invariants in the symmetric algebra

If we do not assume that Card(G) is invertible in K, we still have the implications (ii) $\Longleftrightarrow$ (iii) (cf. Lemma 5) and (ii) $\Longrightarrow$ (i) (cf. Exerc. 8); but the implication (i) $\Longrightarrow$ (ii) is no longer true (Exerc. 9).

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

Cited by

Nothing.

Cites

Exerc. 8
Exerc. 9
Lemma 5