Solvable groups definable in o-minimal structures

Abstract

In this paper we develop group extension theory over an o-minimal structure $\text{N}$ and use it to describe $\text{N}$-definable solvable groups. We prove an o-minimal analogue of the Lie–Kolchin–Mal'cev theorem and we describe $\text{N}$-definable G-modules and $\text{N}$-definable rings.