A virtually 2-step nilpotent group with polynomial geodesic growth
A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpo...
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2022
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1667 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-16672022-10-14T16:01:17Z A virtually 2-step nilpotent group with polynomial geodesic growth Bishop, A. Elder, M. geodesic growth, discrete Heisenberg group 20F65, 20F18, 20F69 A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set. Lugansk National Taras Shevchenko University Australian Research Council 2022-10-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1667 10.12958/adm1667 Algebra and Discrete Mathematics; Vol 33, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1667/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1667/743 Copyright (c) 2022 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2022-10-14T16:01:17Z |
| collection |
OJS |
| language |
English |
| topic |
geodesic growth discrete Heisenberg group 20F65 20F18 20F69 |
| spellingShingle |
geodesic growth discrete Heisenberg group 20F65 20F18 20F69 Bishop, A. Elder, M. A virtually 2-step nilpotent group with polynomial geodesic growth |
| topic_facet |
geodesic growth discrete Heisenberg group 20F65 20F18 20F69 |
| format |
Article |
| author |
Bishop, A. Elder, M. |
| author_facet |
Bishop, A. Elder, M. |
| author_sort |
Bishop, A. |
| title |
A virtually 2-step nilpotent group with polynomial geodesic growth |
| title_short |
A virtually 2-step nilpotent group with polynomial geodesic growth |
| title_full |
A virtually 2-step nilpotent group with polynomial geodesic growth |
| title_fullStr |
A virtually 2-step nilpotent group with polynomial geodesic growth |
| title_full_unstemmed |
A virtually 2-step nilpotent group with polynomial geodesic growth |
| title_sort |
virtually 2-step nilpotent group with polynomial geodesic growth |
| description |
A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1667 |
| work_keys_str_mv |
AT bishopa avirtually2stepnilpotentgroupwithpolynomialgeodesicgrowth AT elderm avirtually2stepnilpotentgroupwithpolynomialgeodesicgrowth AT bishopa virtually2stepnilpotentgroupwithpolynomialgeodesicgrowth AT elderm virtually2stepnilpotentgroupwithpolynomialgeodesicgrowth |
| first_indexed |
2025-12-02T15:25:46Z |
| last_indexed |
2025-12-02T15:25:46Z |
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1850411846960414720 |