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 = Z₂≀Z is a condensation group and has a minimal presentation by generators and relators. The condensation property is achieved by...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153334 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the condensation property of the Lamplighter groups and groups of intermediate growth / M.G. Benli, R. Grigorchuk // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 222–231. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748818990170112 |
|---|---|
| author | Benli, M.G. Grigorchuk, R. |
| author_facet | Benli, M.G. Grigorchuk, R. |
| citation_txt | On the condensation property of the Lamplighter groups and groups of intermediate growth / M.G. Benli, R. Grigorchuk // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 222–231. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 = Z₂≀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 M₂ of marked 2-generated groups consisting mostly of groups of intermediate growth.
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| first_indexed | 2025-12-07T20:57:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153334 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:57:24Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Benli, M.G. Grigorchuk, R. 2019-06-14T03:22:38Z 2019-06-14T03:22:38Z 2014 On the condensation property of the Lamplighter groups and groups of intermediate growth / M.G. Benli, R. Grigorchuk // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 222–231. — Бібліогр.: 13 назв. — англ. 1726-3255 2010 MSC:20F65, 20E08, 20F69, 20F05. https://nasplib.isofts.kiev.ua/handle/123456789/153334 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 = Z₂≀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 M₂ of marked 2-generated groups consisting mostly of groups of intermediate growth. The authors were supported by NSF grant DMS-1207699. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the condensation property of the Lamplighter groups and groups of intermediate growth Article published earlier |
| spellingShingle | On the condensation property of the Lamplighter groups and groups of intermediate growth Benli, M.G. Grigorchuk, R. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153334 |
| work_keys_str_mv | AT benlimg onthecondensationpropertyofthelamplightergroupsandgroupsofintermediategrowth AT grigorchukr onthecondensationpropertyofthelamplightergroupsandgroupsofintermediategrowth |