  Let $S$ be a semiabelian variety over an algebraically closed field, and let
$X$ be an irreducible subvariety not contained in a coset of a proper algebraic
subgroup of $S$. We show that the number of irreducible components of
$[n]^{-1}(X)$ is bounded uniformly in $n$, and moreover that the bound is
uniform in families $X_t$.
  We prove this by purely Galois-theoretic methods. This proof applies in the
more general context of divisible abelian groups of finite Morley rank. In this
latter context, we deduce a definability result under the assumption of the
Definable Multiplicity Property (DMP). We give sufficient conditions for finite
Morley rank groups to have the DMP, and hence give examples where our
definability result holds.
