Let $G$ be a finite abelian group (of odd order if it's significant) acting on sphere $S^2\subset\mathbb{R}^3$. So my question: is it true that $G$ has a fixed point?



Finite group acting on sphere
See 


Fixed points of abelian actions on S2
JOHN FRANKSa1, MICHAEL HANDELa2 and KAMLESH PARWANIa3


(Ergodic Theory and Dynamical Systems, 2007)


