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Algebra Discrete Math., 2014, Volume 17, Issue 2, Pages 222–231 (Mi adm467)  

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.

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Bibliographic databases:

MSC: 20F65, 20E08, 20F69, 20F05
Received: 28.04.2014
Revised: 28.04.2014
Language:

Citation: Mustafa Gökhan Benli, Rostislav Grigorchuk, “On the condensation property of the Lamplighter groups and groups of intermediate growth”, Algebra Discrete Math., 17:2 (2014), 222–231

Citation in format AMSBIB
\Bibitem{BenGri14}
\by Mustafa~G\"okhan~Benli, Rostislav~Grigorchuk
\paper On the condensation property of the Lamplighter groups and groups of intermediate growth
\jour Algebra Discrete Math.
\yr 2014
\vol 17
\issue 2
\pages 222--231
\mathnet{http://mi.mathnet.ru/adm467}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3287930}


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