Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this talk I report on a joint work with Salma Kuhlmann [1], where 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 and, for some special cases, we provide a matrix description of the automorphism group.

[1] S. Kuhlmann and M. Serra, Automorphisms of valued Hahn groups, 2023, arXiv:2302.06290