Submission date: 12 June 2022

Abstract:

We study infinite groups interpretable in V-minimal, power bounded T-convex or certain expansions of p-adically closed fields. We show that every such group G has unbounded exponent and if G is dp-minimal then it is abelian-by-finite.
Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field K, its residue field k (when infinite), its value group Γ, or K/O, where O is the valuation ring.
Our work uses and extends techniques developed in [8] to circumvent elimination of imaginaries.

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Full text arXiv 2206.05677: pdf, ps.