A well-known result of Pillay states that any group interpretable in a differentially closed field can be embedded in an algebraic group. A similar result holds for separably closed fields. Both results rely on similar techniques among which Hrushovski's stable group chunk construction.

In this talk I wish to explain how these result are not so much about stable theories (or stable formulas) but are more precisely related to the presence of a definable generic. As an application, I will explain how one can reinterpret Pillay's classical proof in the setting of separably closed valued fields to show that any group (interpretable in a separably closed valued field) with a definable generic can be embedded in a group definable in the algebraic closure (as a valued field).