Geodesic
Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups
Michelle Bucher1 ; Alexey Talambutsa2
1Université de Genève, Switzerland
2Steklov Mathematical Institute of RAS, Moscow, Russia
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 189-209

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DOI

We prove that for any prime p≥3 the minimal exponential growth rate of the Baumslag–Solitar group BS(1,p) and the lamplighter group Lp​=(Z/pZ)≀Z are equal. We also show that for p=2 this claim is not true and the growth rate of BS(1,2) is equal to the positive root of x3−x2−2, whilst the one of the lamplighter group L2​ is equal to the golden ratio (1+5​)/2. 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.
DOI : 10.4171/ggd/394
Classification : 20-XX
Mots-clés : Exponential growth rate, actions on trees, lamplighter groups

Michelle Bucher  1   ; Alexey Talambutsa  2

1 Université de Genève, Switzerland
2 Steklov Mathematical Institute of RAS, Moscow, Russia 
Michelle Bucher; Alexey Talambutsa. Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 189-209. doi: 10.4171/ggd/394
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     author = {Michelle Bucher and Alexey Talambutsa},
     title = {Minimal exponential growth rates of metabelian {Baumslag{\textendash}Solitar} groups and lamplighter groups},
     journal = {Groups, geometry, and dynamics},
     pages = {189--209},
     year = {2017},
     volume = {11},
     number = {1},
     doi = {10.4171/ggd/394},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/394/}
}
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