This article is cited in 1 paper

RESEARCH ARTICLE

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

Mustafa Gökhan Benli, Rostislav Grigorchuk

Texas A&M University, Mailstop 3368, College Station, TX 77843-3368, USA

Abstract: 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.

MSC: 20F65, 20E08, 20F69, 20F05

Received: 28.04.2014
Revised: 28.04.2014

Language: English

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