It is known that in differentially closed fields of characteristic zero, the ranks of stability $RU$, $RM$ and the topological rank $RH$ need not to be equal. Pillay and Pong have just shown however that the ranks $RU$ and $RM$ coincide in a group definable in this theory. At the opposite, we will show in this paper that the ranks $RM$ and $RH$ of a definable group can also be different, and even lead to non-equivalent notions of generic type.
"Rangs et types de rang maximum dans les corps différentiellement clos." J. Symbolic Logic 67 (3) 1178 - 1188, September 2002. https://doi.org/10.2178/jsl/1190150157