  Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a
$\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is
abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$
type definable subsets there is a minimal one, i.e. their intersection has
bounded index. In fact, the bound is $\leq 2^{|T|}$. We then deal with
2-dependent theories, a wider class of first order theories.
