A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.
