In this note it is understood that all groups are torsion-free abelian groups of finite rank. The author reduces the problem of a description of the groups to the following questions: 1) Classification of strongly indecomposable groups; 2) Classification of categories \(\bar M^ p\); 3) Description of the kinds of groups; 4) Investigation of cones in finite- dimensional lattices. \(\bar M^ p\) is the category of groups where \(Mor(A,B)=Hom_{{\bar {\mathbb{Z}}}_ p}(A,B)\) (\({\bar {\mathbb{Z}}}_ p\) ring of p-adic integers). \(M^ p\) is the category of groups where \(Mor(A,B)=Hom_{{\mathbb{Z}}_ p}(A,B)\) \(({\mathbb{Z}}_ p=\{r/s\in {\mathbb{Q}}|\) \((r,p)=1\})\). The elements of \(Hom_{{\mathbb{Z}}_ p}(A,B)\) are said to be p-homomorphisms, A and B are called groups of the same kind if they are p-isomorphic for every prime p.