Automorphisms of valued Hahn groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911470774648832 |
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| author | Kuhlmann, Salma Serra, Michele |
| author_facet | Kuhlmann, Salma Serra, Michele |
| contents | Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this paper we study the group of valuation (respectively order) preserving automorphisms of a Hahn group $G$. Under the assumption that $G$ satisfies some lifting property, we prove a structure theorem decomposing the automorphism group into a semidirect product of two notable subgroups. We characterise a class of Hahn groups satisfying the aforementioned lifting property. For some special cases we provide a matrix description of the automorphism group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06290 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automorphisms of valued Hahn groups Kuhlmann, Salma Serra, Michele Group Theory Commutative Algebra Logic Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this paper we study the group of valuation (respectively order) preserving automorphisms of a Hahn group $G$. Under the assumption that $G$ satisfies some lifting property, we prove a structure theorem decomposing the automorphism group into a semidirect product of two notable subgroups. We characterise a class of Hahn groups satisfying the aforementioned lifting property. For some special cases we provide a matrix description of the automorphism group. |
| title | Automorphisms of valued Hahn groups |
| topic | Group Theory Commutative Algebra Logic |
| url | https://arxiv.org/abs/2302.06290 |