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The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity

Claudio Nebbia — 2013

Bollettino dell'Unione Matematica Italiana

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 q + 1 > 3 which do not fix any point of the boundary of the tree.

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