Groups, Geometry, and Dynamics
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Scale-multiplicative semigroups and geometry: automorphism groups of treesUdo Baumgartner, Jacqui Ramagge and George A. Willis (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