A scale-multiplicative semigroup in a totally disconnected, locally compact group is one for which the restriction of the scale function on 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. 1051–1075DOI 10.4171/GGD/376