Automorphisms of valued Hahn groups
Salma Kuhlmann, Michele Serra

TL;DR
This paper investigates the automorphism groups of Hahn groups with canonical valuation, providing a structure theorem, characterizations, and matrix descriptions under certain conditions, advancing the understanding of their symmetries.
Contribution
It introduces a decomposition of automorphism groups of Hahn groups satisfying a lifting property, including characterizations and explicit matrix descriptions for special cases.
Findings
Automorphism group decomposes into a semidirect product under certain conditions.
Characterization of Hahn groups satisfying the lifting property.
Matrix descriptions of automorphism groups in special cases.
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 . Under the assumption that 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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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Topology and Set Theory · Functional Equations Stability Results
