  Baer characterized capable finite abelian groups (a group is capable if it is
isomorphic to the quotient of some group by its center) by a condition on the
size of the factors in the invariant factor decomposition (the group must be
noncyclic and the top two invariant factors must be equal). We provide a
different characterization, given in terms of a condition on the lattice of
subgroups. Namely, a finite abelian group G is capable if and only if there
exists a family {H_i} of subgroups of G with trivial intersection, such that
the union generates G and all the quotients G/H_i have the same exponent. The
condition that the family of subgroups generates G may be replaced by the
condition that the family covers G and the condition that the quotients have
the same exponent may be replaced by the condition that the quotients are
isomorphic.
