# Finite $C^{\infty}$-actions are described by a single vector field

### Francisco Javier Turiel

Universidad de Málaga, Spain### Antonio Viruel

Universidad de Málaga, Spain

## Abstract

In this work it is shown that given a connected $C^{\infty}$-manifold $M$ of dimension $\geq 2$ and a finite subgroup $G\subset \operatorname{Diff}(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\times \mathbb{R}$, where the factor $\mathbb{R}$ comes from the flow of $X$.

## Cite this article

Francisco Javier Turiel, Antonio Viruel, Finite $C^{\infty}$-actions are described by a single vector field. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 317–330

DOI 10.4171/RMI/780