On periodic groups of homeomorphisms of the $2$–dimensional sphere

Abstract

We prove that every finitely generated group of homeomorphisms of the $2$–dimensional sphere all of whose elements have a finite order which is a power of $2$ 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 $2$ provided there is an element of even order.