Groups, Geometry, and Dynamics


Full-Text PDF (283 KB) | Metadata | Table of Contents | GGD summary
Volume 10, Issue 3, 2016, pp. 1051–1075
DOI: 10.4171/GGD/376

Scale-multiplicative semigroups and geometry: automorphism groups of trees

Udo Baumgartner[1], Jacqui Ramagge[2] and George A. Willis[3]

(1) University of Wollongong, Australia
(2) University of Sydney, Australia
(3) The University of Newcastle, Callaghan, Australia

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 and shown to correspond to geometric features of the tree.

Keywords: Scale function, tidy subgroup, homogeneous tree, tree ends

Baumgartner Udo, Ramagge Jacqui, Willis George: Scale-multiplicative semigroups and geometry: automorphism groups of trees. Groups Geom. Dyn. 10 (2016), 1051-1075. doi: 10.4171/GGD/376