18.77 (2014)

Let $G$ be a finite $p$-group and let $p^e$ be the largest degree of an irreducible complex representation of $G$. If $p > e$, is it necessarily true that $\bigcap \text{ker}\,\Theta = 1$, where the intersection runs over all irreducible complex representations $\Theta$ of $G$ of degree $p^e$?