On Periodic Groups of Homeomorphisms of the 2–Dimensional Sphere

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. © 2018, Mathematical Sciences Publishers. All rights reserved.