Remark 2

Tag 00O5, permanent. Cite it as [Bourbaki, Tag 00O5].

Algebra, VIII, p. 420, § 21. Linear Representations of Finite Groups

Suppose that the group $G$ is abelian. We saw in the remark of VIII, p. 414 that $\mathscr{I}_K(G)$ can be identified with the set $\operatorname{Hom}(G, \mu_n(K))$ . Likewise, $\mathscr{I}_{K'}(G)$ can be identified with $\operatorname{Hom}(G, \mu_n(K'))$ . With these identifications, the bijection $\varphi_G$ is simply the mapping $\chi \mapsto \varphi \circ \chi$ .

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

VIII, p. 414