Some remarks on dp-minimal groups

TL;DR

This paper investigates the structure of dp-minimal groups, proving that omega-categorical dp-minimal groups are nilpotent-by-finite and that in dp-minimal definably amenable groups, certain types are strongly f-generic.

Contribution

It establishes new structural results for dp-minimal groups, linking model-theoretic properties with algebraic structure and generic types.

Findings

Omega-categorical dp-minimal groups are nilpotent-by-finite.

In dp-minimal definably amenable groups, f-generic global types are strongly f-generic.

Abstract

We prove that $\ omega $-categorical dp-minimal groups are nilpotent-by-finite. We also show that in dp-minimal definably amenable groups, f-generic global types are strongly f-generic.