Nilpotent approximation in the GMT

Some 13 years ago A. Agrachev asked whether numerical moduli abundant in the GMT appeared also on the level of nilpotent approximations. We work towards a negative answer to this question, discovering surprising phenomena under way. Phenomena leading to, no wonder, new questions. (The talk will start with a brief recalling of the basic stratification of the stages of the GMT. That recalling will be given in two equivalent languages: - kinematic of F.Jean and differential geometric of ... E.Cartan.)