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A group of automorphisms of the rooted dyadic tree and associated Gelfand pairs. (English) Zbl 1167.05033
Summary: We study the group $$G$$ of automorphisrns of the rooted dyadic tree generated by translation by 1 and multiplication by an odd integer $$q$$, showing that $$G$$ admits a self-similar presentation and it is isomorphic to the Baumslag-Solitar group $$BS_q$$. Moreover, we show that the action of $$G$$ on each level of the tree gives rise to a Gelfand pair.

##### MSC:
 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C05 Trees
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##### References:
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