Definable Groups for Dependent and 2-Dependent Theories - Shelah, Saharon (Sarajevo Journal of Mathematics, 2017)
Let T be a (first order complete) dependent theory, a κ-saturated model of T and G a definable subgroup which is abelian. Among subgroups of bounded index which are the union of < κ type-definable subsets there is a minimal one, i.e. their intersection has bounded index. See history in Sh:876. We then deal with definable groups for 2-dependent theories, a wider class of first order theories proving that for many pairs (M,N) of models, the minimal bounded subgroup definable over M N is the intersection of the minimal ones for M and for N.