Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups
Michelle Bucher
Université de Genève, SwitzerlandAlexey Talambutsa
Steklov Mathematical Institute of RAS, Moscow, Russia
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Abstract
We prove that for any prime the minimal exponential growth rate of the Baumslag–Solitar group BS and the lamplighter group are equal. We also show that for this claim is not true and the growth rate of BS is equal to the positive root of , whilst the one of the lamplighter group is equal to the golden ratio . The latter value also serves to show that the lower bound of A.Mann from[9] for the growth rates of non-semidirect HNN extensions is optimal.
Cite this article
Michelle Bucher, Alexey Talambutsa, Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups. Groups Geom. Dyn. 11 (2017), no. 1, pp. 189–209
DOI 10.4171/GGD/394