Milieu et symétrie, une étude de la convexité dans les groupes sans involutions

Motivated by a recent result of Olivier Frécon, we develop a general notion of convex set in a group, which behaves decently in the absence of involutions, and in particular in a group of finite Morley rank without involutions. We show that the geometry of a minimal bad group degenerates, its only convex subsets being points, lines and the whole space.