The derived subgroup of linear and simply-connected o-minimal groups

TL;DR

This paper proves that the derived subgroup of linear and simply-connected definable groups in o-minimal structures is also definable, extending previous results from the semialgebraic case.

Contribution

It extends the definability of the derived subgroup to linear and simply-connected groups within o-minimal structures, broadening the scope of prior work.

Findings

Derived subgroup of linear definable groups is definable.

Derived subgroup of simply-connected definable groups is definable.

Abstract

We show that the derived subgroup of a linear definable group in an o-minimal structure is also definable, extending the semialgebraic case proved by A. Pillay. We also show the definability of the derived subgroup in case that the group is simply-connected.