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arXiv · 2302.06290

Automorphisms of valued Hahn groups

Salma Kuhlmann·Michele Serra
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Abstract

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.

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Salma Kuhlmann, Michele Serra. 2023-02-13. Automorphisms of valued Hahn groups. https://arxiv.org/abs/2302.06290

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