  We show that, given a continuous action $\alpha$ of a locally compact group
$G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_{\alpha} G)$ is
contained in $M\rtimes_{\alpha} H$ where $H$ is the subgroup of elements acting
without spectral gap. As a corollary, we answer a question of Marrakchi and
Vaes by showing that if $M$ is semifinite and $\alpha_g$ is not approximately
inner for all $g\neq 1$, then $M'\cap (M\rtimes_{\alpha} G)=\mathbb{C}$.
