Period three actions on lens spaces

Abstract

We prove that a free ${\mathbb{Z}}_3$ action on a lens space is standard. This extends to lens spaces earlier work of Maher and Rubinstein on ${\mathbb{Z}}_3$ actions on $S^3$. It follows using previously known results that a free action of a group of order $2^a{3}^b$ on $S^3$ is standard.