11.33 (1990)

Let $G(q)$ be a simple Chevalley group over a field of order $q$. Prove that there exists $m$ such that:
$\qquad$ a) the restriction of every non-one-dimensional complex representation of $G(q^m)$ to $G(q)$ contains all irreducible representations of $G(q)$ as composition factors.
$\qquad$ b) the restriction of every non-one-dimensional representation of $G(q^m)$ over a field of prime characteristic not dividing $q$ to $G(q)$ contains all irreducible representations of $G(q)$ as composition factors.