This dissertation is devoted to the discussion of a new type of subgroup in torsion-free abelian groups. It is motivated by the notion of balanced subgroups. Our subgroups, called ultrabalanced subgroups, are more restrictive, but they still share many of the relevant properties of balancedness. After defining ultrabalanced subgroups, we exhibit examples, give characterizations and prove some of their important properties. Ultrabalanced-projectives and ultrabalanced-injectives are discussed. At last, we introduce the concept of ultrabalanced-projective dimensions and give some fundamental results
