A Note on the Amenable Subgroups of PSL (2, R).
In this paper we describe the groups of isometries acting transitively on the homogeneous tree of degree three. This description implies that the following three properties are equivalent: amenability, non-unimodularity and action without inversions. Moreover, we exhibit examples of non-unimodular transitive groups of isometries of a homogeneous tree of degree which do not fix any point of the boundary of the tree.
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