Superrosy dependent groups having finitely satisfiable generics

We develop a basic theory of rosy groups and we study groups of small U ‏ -rank satisfying NIP and having finitely satisfiable generics: U ‏ -rank 1 implies that the group is abelian-by-finite, U ‏ -rank 2 implies that the group is solvable-by-finite, U ‏ -rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.