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Algebra and Discrete Mathematics, 2014, Volume 17, Issue 2, Pages 222–231
(Mi adm467)
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This article is cited in 1 scientific paper (total 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.
Received: 28.04.2014 Revised: 28.04.2014
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
Linking options:
https://www.mathnet.ru/eng/adm467 https://www.mathnet.ru/eng/adm/v17/i2/p222
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Abstract page: | 373 | Full-text PDF : | 70 | References: | 42 |
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