2024-11-0920180933-584610.1007/s00153-017-0565-42-s2.0-85020296096http://dx.doi.org/10.1007/s00153-017-0565-4https://hdl.handle.net/20.500.14288/6459In this paper, we study an algebraically closed field expanded by two unary predicates denoting an algebraically closed proper subfield k and a multiplicative subgroup . This will be a proper expansion of algebraically closed field with a group satisfying the Mann property, and also pairs of algebraically closed fields. We first characterize the independence in the triple . This enables us to characterize the interpretable groups when is divisible. Every interpretable group H in is, up to isogeny, an extension of a direct sum of k-rational points of an algebraic group defined over k and an interpretable abelian group in by an interpretable group N, which is the quotient of an algebraic group by a subgroup , which in turn is isogenous to a cartesian product of k-rational points of an algebraic group defined over k and an interpretable abelian group in .MathematicsLogicJournal Article1432-0665428317500002Q33205