TITLE: Reference for this theorem in representation theory?
QUESTION [16 upvotes]: Let $G$ be a finite group and $\chi$ be an irreducible character of
$G$ (characteristic zero algebraically closed base field). If $H$ is
the kernel of $\chi$ then the irreducible representations of $G/H$
are exactly all the irreducible constituents of all tensor powers
$\chi^n$.

Do you know any reference for this theorem?
Is it also working in positive characteristic?
Is it also working for some infinite groups? (maybe some special
classes: reductive, Lie type, etc)

Thank you very much!

REPLY [3 votes]: Explicit references: 

BURNSIDE, W. Theory of Groups of Finite Order, 2nd ed. Cambridge University
Press, Cambridge, 1911; Dover, New York, 1955.  (§226 Theorem IV)   
BRAUER, R. A note on theorems of Burnside and Blichfeldt. Proc. Am. Math.
soc. 15 (1964), 31-34.
(Theorem 1)  

Generalizations: 

STEINBERG, R. Complete sets of representations of algebras. Proc. Am. Math.
Soc. 13 (1962), 746-747.
RIEFFEL, M.A. Burnside’s Theorem for Representations of Hopf Algebras. J. Alg. 6 (1967), 123-130.