Nebbia, Claudio:
The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity
Bollettino dell'Unione Matematica Italiana Serie 9 6 (2013), fasc. n.3, p. 565-577, (English)
pdf (335 Kb), djvu (146 Kb). | MR 3202840
Sunto
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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