Corollary 2

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

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

Suppose that the group G is finite and that $|G|$ is invertible in K. An exact sequence of K[G]-modules splits if and only if it splits as an exact sequence of K-modules.

Given an exact sequence of K[G]-modules

0 // ${M'}^f$ // M // $M''$ // $0$ ,

it suffices to apply Theorem 1 to the image of the morphism $f$ .

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

Corollary 3, § 21

Cites

Theorem 1