Geodesic
On the condensation property of the Lamplighter groups and groups of intermediate growth
Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 222-231

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group $L = \mathbb{Z}_2 \wr \mathbb{Z}$ is a condensation group and has a minimal presentation by generators and relators. The condensation property is achieved by showing that $L$ belongs to a Cantor subset of the space $\mathcal{M}_2$ of marked $2$-generated groups consisting mostly of groups of intermediate growth.
Keywords: Lamplighter groups; groups of intermediate growth; space of marked groups; condensation groups. 
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     author = {Mustafa G\"okhan Benli and Rostislav Grigorchuk},
     title = {On the condensation property of the {Lamplighter} groups and groups of intermediate growth},
     journal = {Algebra and discrete mathematics},
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     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a3/}
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Mustafa Gökhan Benli; Rostislav Grigorchuk. On the condensation property of the Lamplighter groups and groups of intermediate growth. Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 222-231. http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a3/