Scale-multiplicative semigroups and geometry: automorphism groups of trees

  • Udo Baumgartner

    University of Wollongong, Australia
  • Jacqui Ramagge

    University of Sydney, Australia
  • George A. Willis

    The University of Newcastle, Callaghan, Australia

Abstract

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

Cite this article

Udo Baumgartner, Jacqui Ramagge, George A. Willis, Scale-multiplicative semigroups and geometry: automorphism groups of trees. Groups Geom. Dyn. 10 (2016), no. 3, pp. 1051–1075

DOI 10.4171/GGD/376