  We show that if $P$ is a $PD_3$-complex and $g\in\pi_1(P)$ has finite order
$>1$ and infinite centraliser then $\pi_1(P)$ retracts onto
$Z/2Z\oplus\mathbb{Z}$. If $P$ is an irreducible closed 3-manifold then it
follows from the Projective Plane Theorem that $P\cong{RP^2}\times{S^1}$.
