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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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