On a question of Navarro and Wolf

In this note, we answer a question raised by Navarro and Wolf in [4]. We show that if $P$ is a Sylow $p$-subgroup of a finite group $G$ where $p$ is an odd prime, then $G'\cap N_G(P)\subseteq P$ if and only if $p$ divides the degree of every irreducible non-linear $p$-Brauer character of $G$.