We prove that every finitely generated group of homeomorphisms of the –dimensional sphere all of whose elements have a finite order which is a power of and is such that there exists a uniform bound for the orders of the group elements is finite. We prove a similar result for groups of area-preserving homeomorphisms without the hypothesis that the orders of group elements are powers of provided there is an element of even order.
"On periodic groups of homeomorphisms of the $2$–dimensional sphere." Algebr. Geom. Topol. 18 (7) 4093 - 4107, 2018. https://doi.org/10.2140/agt.2018.18.4093