We define a notion of genericity for arbitrary subgroups of groups interpretable in a simple theory, and show that a type generic for such a group is generic for the minimal hyperdefinable supergroup (the definable hull). In particular, at least one generic type of the definable hull is finitely satisfiable in the original subgroup. If the subgroup is a subfield, then the additive and the multiplicative definable hull both have bounded index in the smallest hyperdefinable superfield.
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1129642130
Digital Object Identifier: doi:10.2178/jsl/1129642130
Mathematical Reviews number (MathSciNet): MR2194252
Zentralblatt MATH identifier: 1104.03025