Scale-multiplicative semigroups and geometry: automorphism groups of trees

Udo Baumgartner, Jacqui Ramagge, George A. Willis

Published 2013-12-04Version 1

A scale-multiplicative semigroup in a totally disconnected, locally compact group $G$ is one for which the restriction of the scale function on $G$ is multiplicative. The maximal scale-multiplicative semigroups in groups acting 2-transitively on the set of ends of trees without leaves are determined in this paper and shown to correspond to geometric features of the tree.