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 so that there exists a uniform bound for the order of 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.

14 pages

Cited by in corpus (1)

• The Burnside problem for ${\text{Diff}}_{\text{Vol}}({\mathbb{S}}^2)$