Conjugator length of locally compact groups of Euclidean isometries
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909671885897728 |
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| author | Rego, Yuri Santos Schwer, Petra |
| author_facet | Rego, Yuri Santos Schwer, Petra |
| contents | We consider locally compact subgroups $H$ of the full isometry group $\mathrm{Isom}(\mathbb{E}^n)$ of Euclidean $n$-space which respect the splitting into an orthogonal and a translation subgroup. We prove that the conjugator length function of such groups grows linearly. Our theorem applies, in particular, to the Lie group $\mathrm{Isom}(\mathbb{E}^n)$ itself but also to affine Coxeter groups and to split crystallographic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugator length of locally compact groups of Euclidean isometries Rego, Yuri Santos Schwer, Petra Group Theory 20F65, 20E45, 20F10, 22E25, 20F55 We consider locally compact subgroups $H$ of the full isometry group $\mathrm{Isom}(\mathbb{E}^n)$ of Euclidean $n$-space which respect the splitting into an orthogonal and a translation subgroup. We prove that the conjugator length function of such groups grows linearly. Our theorem applies, in particular, to the Lie group $\mathrm{Isom}(\mathbb{E}^n)$ itself but also to affine Coxeter groups and to split crystallographic groups. |
| title | Conjugator length of locally compact groups of Euclidean isometries |
| topic | Group Theory 20F65, 20E45, 20F10, 22E25, 20F55 |
| url | https://arxiv.org/abs/2507.01268 |