On the condensation property of the Lamplighter groups and groups of intermediate growth
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 condensat...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1032 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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