Amenable actions of nonamenable groups
Academic Article
Overview
Identity
Additional Document Info
Other
View All
Overview
abstract
We present two methods of constructing amenable (in the sense of Greenleaf) actions of nonamenable groups. In the first part of the paper, we construct a class of faithful transitive amenable actions of the free group using Schreier graphs. In the second part, we show that every finitely generated residually finite group can be embedded into a bigger residually finite group, which acts level-transitively on a locally finite rooted tree, so that the induced action on the boundary of the tree is amenable on every orbit. Bibliography: 25 titles. Springer Science+Business Media, Inc. 2007.