  Let $G$ be a finite abelian group and $A$ be a subset of $G$. We say that $A$
is complete if every element of $G$ can be represented as a sum of different
elements of $A$. In this paper, we study the following question: {\it What is
the structure of a large incomplete set ?} The typical answer is that such a
set is essentially contained in a maximal subgroup. As a by-product, we obtain
a new proof for several earlier results.
