Explicit references:

• BURNSIDE, W. Theory of Groups of Finite Order, 2nd ed. Cambridge University Press, Cambridge, 1911; Dover, New York, 1955. (Chapter XV, 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.

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.