Abstract
Classically a colored tree is associated to any p-adic groups of rank one. For some of these, subgroups acting simply transitively on vertices of given color are constructed. In fewer case, the same can be done for edges.
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Choucroun, F.M. Sous-groupes discrets des groupes p-adiques de rang un et arbres de Bruhat-Tits. Israel J. Math. 93, 195–219 (1996). https://doi.org/10.1007/BF02761103
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DOI: https://doi.org/10.1007/BF02761103