  A group $G$ is said to be cut if, for every $g \in G$, each generator of $<
\! g \! >$ is conjugated to either $g$ or $g^{-1}$. It is conjectured that a
Sylow 3-subgroup $P$ of a cut group $G$ is cut. We prove that this is true if
$|G|$ is odd.
