Burnside problem for measure preserving groups of toral homeomorphisms and for 2-groups of toral homeomorphisms

الأصل · EN

A group G is said to be periodic if for any g∈ G there exists a positive integer n with gⁿ=id. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure μ is finite. Moreover if the group consists in homeomorphisms isotopic to the identity, then it is abelian and acts freely on T². In the Appendix, we show that every finitely generated 2-group of toral homeomorphisms is finite.