Ordered groups of formal series, and a conjugacy problem
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916946330517504 |
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| author | Bagayoko, Vincent |
| author_facet | Bagayoko, Vincent |
| contents | Given an ordered field $\mathbb{T}$ of formal series over an ordered field $\mathbf{R}$ equipped with a composition law $\circ \colon \mathbb{T} \times \mathbb{T}^{>\mathbb{R}} \longrightarrow \mathbb{T}$, we give conditions for $(\mathbb{T}^{>\mathbb{R}},\circ)$ to be a group. We show that classical fields of transseries and hyperseries satisfy these conditions. We then give further conditions on $\mathbb{T}$ under which $(\mathbb{T}^{>\mathbb{R}},\circ,<)$ is a linearly ordered group with exactly three conjugacy classes, and solve the open problem of existence of such a group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ordered groups of formal series, and a conjugacy problem Bagayoko, Vincent Logic Group Theory Given an ordered field $\mathbb{T}$ of formal series over an ordered field $\mathbf{R}$ equipped with a composition law $\circ \colon \mathbb{T} \times \mathbb{T}^{>\mathbb{R}} \longrightarrow \mathbb{T}$, we give conditions for $(\mathbb{T}^{>\mathbb{R}},\circ)$ to be a group. We show that classical fields of transseries and hyperseries satisfy these conditions. We then give further conditions on $\mathbb{T}$ under which $(\mathbb{T}^{>\mathbb{R}},\circ,<)$ is a linearly ordered group with exactly three conjugacy classes, and solve the open problem of existence of such a group. |
| title | Ordered groups of formal series, and a conjugacy problem |
| topic | Logic Group Theory |
| url | https://arxiv.org/abs/2509.09186 |