17.74 (2010)

Let $G$ be a finite simple group of Lie type defined over a field of characteristic $p$ whose Lie rank is at least three, and $V$ an absolutely irreducible $G$-module over a field of characteristic that does not divide $p$. It is true that the split extension of $V$ by $G$ must contain an element whose order is distinct from the order of any element of $G$? The case of $G = U_n(p^m)$ is of special interest.