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 |
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Lugansk National Taras Shevchenko University
2018
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| 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| _version_ | 1856543416122343424 |
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| author | Benli, Mustafa Gökhan Grigorchuk, Rostislav |
| author_facet | Benli, Mustafa Gökhan Grigorchuk, Rostislav |
| author_sort | Benli, Mustafa Gökhan |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:11:00Z |
| description | 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. |
| first_indexed | 2026-02-08T07:59:07Z |
| format | Article |
| id | admjournalluguniveduua-article-1032 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:59:07Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-10322018-04-26T02:11:00Z On the condensation property of the Lamplighter groups and groups of intermediate growth Benli, Mustafa Gökhan Grigorchuk, Rostislav Lamplighter groups; groups of intermediate growth; space of marked groups; condensation groups 20F65, 20E08, 20F69, 20F05 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. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1032 Algebra and Discrete Mathematics; Vol 17, No 2 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1032/555 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Lamplighter groups groups of intermediate growth space of marked groups condensation groups 20F65 20E08 20F69 20F05 Benli, Mustafa Gökhan Grigorchuk, Rostislav On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title | On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title_full | On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title_fullStr | On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title_full_unstemmed | On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title_short | On the condensation property of the Lamplighter groups and groups of intermediate growth |
| title_sort | on the condensation property of the lamplighter groups and groups of intermediate growth |
| topic | Lamplighter groups groups of intermediate growth space of marked groups condensation groups 20F65 20E08 20F69 20F05 |
| topic_facet | Lamplighter groups groups of intermediate growth space of marked groups condensation groups 20F65 20E08 20F69 20F05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1032 |
| work_keys_str_mv | AT benlimustafagokhan onthecondensationpropertyofthelamplightergroupsandgroupsofintermediategrowth AT grigorchukrostislav onthecondensationpropertyofthelamplightergroupsandgroupsofintermediategrowth |