Coarse length can be unbounded in 3-step nilpotent Lie groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916843137007616 |
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| author | Stoll, Michael |
| author_facet | Stoll, Michael |
| contents | In "On the asymptotics of the growth of 2-step nilpotent groups" (J. London Math. Soc. (2), 58 (1998)), we remarked that, contrary to 2-step nilpotent simply connected Lie groups, in 3-step nilpotent simply connected Lie groups it is possible that `$\mathbb{R}$-words' in the given generators cannot be replaced by an equally long $\mathbb{R}$-word representing the same group element and having a bounded number of direction changes. In this note, we present an example for this phenomenon. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_10408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarse length can be unbounded in 3-step nilpotent Lie groups Stoll, Michael Group Theory 20F05, 20F18, 20F65, 22E25 In "On the asymptotics of the growth of 2-step nilpotent groups" (J. London Math. Soc. (2), 58 (1998)), we remarked that, contrary to 2-step nilpotent simply connected Lie groups, in 3-step nilpotent simply connected Lie groups it is possible that `$\mathbb{R}$-words' in the given generators cannot be replaced by an equally long $\mathbb{R}$-word representing the same group element and having a bounded number of direction changes. In this note, we present an example for this phenomenon. |
| title | Coarse length can be unbounded in 3-step nilpotent Lie groups |
| topic | Group Theory 20F05, 20F18, 20F65, 22E25 |
| url | https://arxiv.org/abs/2507.10408 |