On the condensation property of the Lamplighter groups and groups of intermediate growth

Mustafa Gökhan Benli, Rostislav Grigorchuk


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.


Lamplighter groups; groups of intermediate growth; space of marked groups; condensation groups

Full Text:



  • There are currently no refbacks.