Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Bagayoko, Vincent
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414486606
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