# Definable Topological Dynamics for Trigonalizable Algebraic Groups over Qp

## TL;DR

This paper investigates the topological dynamics of trigonalizable algebraic groups over Qp, showing that all f-generic types are almost periodic and describing their structure within the type space.

## Contribution

It provides a detailed description of f-generic types for trigonalizable algebraic groups over Qp and proves their almost periodicity, addressing a key open question.

## Key findings

- All f-generic types are almost periodic.
- Description of f-generic types in trigonalizable algebraic groups.
- The union of minimal subflows is closed.

## Abstract

We study the flow (G(Qp); SG(Qp)) of trigonalizable algebraic group acting on its type space, focusing on the problem raised in [17] of whether weakly generic types coincide with almost periodic types if the group has global definable f-generic types, equivalently whether the union of minimal subflows of a suitable type space is closed. We will give a description of of f-generic types of trigonalizable algebraic groups, and prove that every f-generic type is almost periodic.