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Preprint Number 2345

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2345. Salma Kuhlmann, Michele Serra
Automorphisms of valued Hahn groups

Submission date: 13 February 2023


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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Full text arXiv 2302.06290: pdf, ps.

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