The derived subgroup of linear and simply-connected o-minimal groups (Q1732885)

The present paper studies groups definable over an o-minimal expansion of a real closed field, so-called o-minimal groups. The author proves that the derived subgroup (the commutator subgroup) of a connected o-minimal group which is either linear or simply-connected is definable. In addition, the author proves an o-minimal version of a classical result by A. Mal'tsev concerning the existence of cross-section of projection maps of quotients of simply-connected Lie groups.