Corollary 3

Tag 00NM, permanent. Cite it as [Bourbaki, Tag 00NM].

Algebra, VIII, p. 401, § 21. Linear Representations of Finite Groups

Suppose that the group G is finite and that $|G|$ is invertible in K. A K[G]-module is projective if and only if it is projective as a K-module.

Let P be a K[G]-module. If P is a direct factor of a free K[G]-module M, then it is a fortiori a direct factor of the free K-module M. The converse follows from Corollary 2, in view of II, §2, No. 2, p. 231, Proposition 4, d).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

II, §2, No. 2, p. 231, Proposition 4 not in this corpus
Corollary 2